]>
2011
4
2
ISSN 2008-1898
87
ON THE \((p; q)\)-GROWTH OF ENTIRE FUNCTION SOLUTIONS OF HELMHOLTZ EQUATION
ON THE \((p; q)\)-GROWTH OF ENTIRE FUNCTION SOLUTIONS OF HELMHOLTZ EQUATION
en
en
The \((p; q)\)-growth of entire function solutions of Helmholtz equations in \(R^2\) has been studied. We obtain some lower bounds on order and type
through function theoretic formulae related to those of associate. Our results
extends and improve the results studied by McCoy [10].
92
101
DEVENDRA
KUMAR
Department of Mathematics
Research and Post Graduate Studies, M.M.H. College
India
Index-pair \((p
q)\)
Bergman integral operator
order and type
Helmholtz equation and entire function.
Article.1.pdf
[
[1]
S. Bergman, Integral operators in the Theory of Linear Partial Differential Equations, Ergebnisse der Mathematik und ihrer Grenzgebiete, Band 23, Springer-Verlag, New Yok (1969)
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R. P. Gilbert, Function Theoretic Methods in Partial Differential Equations, Math. in Science and Engineering Vol. 54, Academic Press, New York (1969)
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R. P. Gilbert, D. L. Colton, Integral operator methods in biaxial symmetric potential theory, Contrib. Differential Equations , 2 (1963), 441-456
##[4]
R. P. Gilbert, D. L. Colton, Singularities of solutions to elliptic partial differential equations, Quarterly J. Math., 19 (1968), 391-396
##[5]
O. P. Juneja, G. P. Kapoor, S. K. Bajpai , On the (p; q)-order and lower (p; q)-order of an entire function, J. Reine Angew. Math. , 282 (1976), 53-67
##[6]
O. P. Juneja, G. P. Kapoor, S. K. Bajpai , On the (p; q)-type and lower (p; q)-type of an entire function, J. Reine Angrew. Math. , 290 (1977), 180-190
##[7]
E. O. Kreyszig, M. Kracht, Methods of Complex Analysis in Partial Differential Equations with Applications, Canadian Math. Soc. Series of Monographs and Adv. Texts, John Wiley and Sons , New York (1988)
##[8]
P. A. McCoy, Polynomial approximation and growth of generalized axisymmetric potentials, Canadian J. Math., XXXI (1979), 49-59
##[9]
P. A. McCoy, Optimal approximation and growth of solution to a class of elliptic differential equations, J. Math. Anal. Appl. , 154 (1991), 203-211
##[10]
P. A. McCoy, Solutions of the Helmholtz equation having rapid growth, Complex Variables and Elliptic Equations , 18 (1992), 91-101
]
EXISTENCE OF GLOBAL SOLUTIONS FOR IMPULSIVE FUNCTIONAL DIFFERENTIAL EQUATIONS WITH NONLOCAL CONDITIONS
EXISTENCE OF GLOBAL SOLUTIONS FOR IMPULSIVE FUNCTIONAL DIFFERENTIAL EQUATIONS WITH NONLOCAL CONDITIONS
en
en
In this paper, we study the existence of global solutions for a class
of impulsive abstract functional differential equation with nonlocal conditions.
The results are obtained by using the Leray-Schauder alternative fixed point
theorem. An example is provided to illustrate the theory.
102
114
S.
SIVASANKARAN
Department of Mathematics, University College
Sungkyunkwan University
South Korea
sdsiva@gmail.com
M. MALLIKA
ARJUNAN
Department of Mathematics
Karunya University
India
arjunphd07@yahoo.co.in
V.
VIJAYAKUMAR
Department of Mathematics
Info Institute of Engineering
India
vijaysarovel@gmail.com
Impulsive functional differential equations
mild solutions
global solutions
semigroup theory.
Article.2.pdf
[
[1]
H. Akca, A. Boucherif, V. Covachev, Impulsive functional differential equations with nonlocal conditions, Inter. J. Math. Math. Sci., 29:5 (2002), 251-256
##[2]
A. Anguraj, K. Karthikeyan , Existence of solutions for impulsive neutral functional differential equations with nonlocal conditions, Nonlinear Anal., 70(7) (2009), 2717-2721
##[3]
A. Anguraj, M. Mallika Arjunan, Existence and uniqueness of mild and classical solutions of impulsive evolution equations, Electronic Journal of Differential Equations, 111 (2005), 1-8
##[4]
A. Anguraj, M. Mallika Arjunan, Existence results for an impulsive neutral integro- differential equations in Banach spaces, Nonlinear Studies, 16(1) (2009), 33-48
##[5]
D. D. Bainov, P. S. Simeonov, Impulsive Dierential Equations: Periodic Solutions and Applications, Longman Scientific and Technical Group, England (1993)
##[6]
K. Balachandran, J. Y. Park, M. Chandrasekaran, Nonlocal Cauchy problem for delay integrodifferential equations of Sobolve type in Banach spaces, Appl. Math. Lett., 15(7) (2002), 845-854
##[7]
M. Benchohra, J. Henderson, S. K. Ntouyas, Existence results for impulsive multi- valued semilinear neutral functional differential inclusions in Banach spaces, J. Math. Anal. Appl., 263(2) (2001), 763-780
##[8]
M. Benchohra, J. Henderson, S. K. Ntouyas, Impulsive neutral functional differential inclusions in Banach spaces, Appl. Math. Lett., 15(8) (2002), 917-924
##[9]
M. Benchohra, A. Ouahab, Impulsive neutral functional differential equations with variable times, Nonlinear Anal., 55(6) (2003), 679-693
##[10]
M. Benchohra, J. Henderson, S. K. Ntouyas, Impulsive Differential Equations and Inclusions, Hindawi Publishing Corporation, New York (2006)
##[11]
L. Byszewski, Theorems about the existence and uniqueness of solutions of a semilinear evolution nonlocal Cauchy problem, J. Math. Anal. Appl., 162(2) (1991), 494-505
##[12]
L. Byszewski , Existence, uniqueness and asymptotic stability of solutions of abstract nonlocal Cauchy problems, Dynam. Systems Appl., 5(4) (1996), 595-605
##[13]
L. Byszewski, H. Akca, Existence of solutions of a semilinear functional differential evolution nonlocal problem, Nonlinear Anal., 34(1) (1998), 65-72
##[14]
L. Byszewski, H. Akca, On a mild solution of a semilinear functional-differential evolution nonlocal problem, J. Appl. Math. Stochastic Anal., 10(3) (1997), 265-271
##[15]
Y. K. Chang, A. Anguraj, M. Mallika Arjunan, Existence results for non-densely defined neutral impulsive differential inclusions with nonlocal conditions, J. Appl. Math. Comput., 28 (2008), 79-91
##[16]
Y. K. Chang, A. Anguraj, M. Mallika Arjunan, Existence results for impulsive neutral functional differential equations with infinite delay, Nonlinear Anal.: Hybrid Systems, 2(1) (2008), 209-218
##[17]
Y. K. Chang, V. Kavitha, M. Mallika Arjunan, Existence results for impulsive neutral differential and integrodifferential equations with nonlocal conditions via fractional operators, Nonlinear Anal.: Hybrid Systems, 4(1) (2010), 32-43
##[18]
C. Cuevas, E. Hernández, M. Rabelo, The existence of solutions for impulsive neutral functional differential equations, Comput. Math. Appl., 58 (2009), 744-757
##[19]
A. Granas, J. Dugundji, Fixed Point Theory, Springer-Verlag, New York (2003)
##[20]
E. Hernández, Existence results for partial neutral integrodifferential equations with nonlocal conditions, Dynam. Systems Appl., 11(2) (2002), 241-252
##[21]
E. Hernández, S. M. Tanaka Aki, Global solutions for abstract functional differential equations with nonlocal conditions, Electronic Journal of Qualitative Theory of Differential Equations, 50 (2009), 1-8
##[22]
E. Hernández, M. McKibben, H. Henríquez, Existence results for abstract impulsive second order neutral functional differential equations, Nonlinear Anal., 70 (2009), 2736-2751
##[23]
E. Hernández, M. Pierri, G. Goncalves, Existence results for an impulsive abstract partial differential equations with state-dependent delay, Comput. Math. Appl. , 52 (2006), 411-420
##[24]
E. Hernández, M. Mckibben, Some comments on: ''Existence of solutions of abstarct nonlinear second-order neutral functional integrodifferential equations'' , Comput. Math. Appl., 50(5-6) (2005), 655-669
##[25]
E. Hernández, M. Rabello, H. R. Henriquez , Existence of solutions for impulsive partial neutral functional differential equations, J. Math. Anal. Appl., 331 (2007), 1135-1158
##[26]
E. Hernández, H. R. Henriquez, Impulsive partial neutral differential equations, Appl. Math. Lett., 19 (2006), 215-222
##[27]
Y. Hino, S. Murakami, T. Naito, In Functional-differential equations with infinite delay, Lecture notes in Mathematics, 1473, Springer-Verlog, Berlin (1991)
##[28]
G. L. Karakostas, P. Ch. Tsamatos, Suficient conditions for the existence of nonnegative solutions of a nonlocal boundary value problem, Appl. Math. Lett., 15(4) (2002), 401-407
##[29]
V. Lakshmikantham, D. D. Bainov, P. S. Simeonov, Theory of Impulsive Differential Equations, World Scientific, Singapore (1989)
##[30]
J. H. Liu, Nonlinear impulsive evolution equations, Dynam. Contin. Discrete Impuls. Sys., 6 (1999), 77-85
##[31]
J. Liang, J. H. Liu, Ti-Jun Xiao, Nonlocal impulsive problems for nonlinear differential equations in Banach spaces, Math. Comput. Model., 49 (2009), 798-804
##[32]
R. H. Martin, Nonlinear Operators and Differential Equations in Banach Spaces, Robert E. Krieger Publ. Co., Florida (1987)
##[33]
S. K. Ntouyas, P. Tsamatos, Global existence for semilinear evolution equations with nonlocal conditions, J. Math. Anal. Appl., 210 (1997), 679-687
##[34]
W. E. Olmstead, C. A. Roberts, The one-dimensional heat equation with a non- local initial condition, Appl. Math. Lett., 10(3) (1997), 84-94
##[35]
J. Y. Park, K. Balachandran, N. Annapoorani, Existence results for impulsive neutral functional integrodifferential equations with infinite delay, Nonlinear Analysis, 71 (2009), 3152-3162
##[36]
A. Pazy, Semigroups of linear operators and applications to partial differential equations, Applied Mathematical Sciences, 44, Springer-Verlag, New York-Berlin (1983)
##[37]
Y. V. Rogovchenko, Impulsive evolution systems: Main results and new trends, Dynam. Contin. Discrete Impuls. Syst., 3(1) (1997), 57-88
##[38]
Y. V. Rogovchenko, Nonlinear impulsive evolution systems and application to population models, J. Math. Anal. Appl., 207(2) (1997), 300-315
##[39]
A. M. Samoilenko, N. A. Perestyuk, Impulsive Differential Equations , World Scientific, Singapore (1995)
]
CONDITIONING OF THREE-POINT BOUNDARY VALUE PROBLEMS ASSOCIATED WITH FIRST ORDER MATRIX LYAPUNOV SYSTEMS
CONDITIONING OF THREE-POINT BOUNDARY VALUE PROBLEMS ASSOCIATED WITH FIRST ORDER MATRIX LYAPUNOV SYSTEMS
en
en
This paper deals with the study of conditioning for three-point
boundary value problems associated with first order matrix Lyapunov systems,
with the help of Kronecker product of matrices. Further, we obtain the close
relationship between the stability bounds of the problem on one hand , and
the growth behavior of the fundamental matrix solution on the other hand.
115
125
M. S. N.
MURTY
Department of Applied Mathematics
Achrya Nagarjuna University-Nuzvid Campus
India
drmsn2002@gmail.com
D.
ANJANEYULU
Department of Applied Mathematics
Achrya Nagarjuna University-Nuzvid Campus
India
G. SURESH
KUMAR
Department of Mathematics (FED-II)
K L University
India
gsk006@yahoo.com
Lyapunov system
boundary value problem
Kronecker product
condition number.
Article.3.pdf
[
[1]
F. R. De Hoog, R. M. M. Mattheije, On dichotomy and well conditioning in boundary value problem, SIAM J. Numer. Anal., 24 (1987), 89-105
##[2]
A. Graham, Kronecker Products and Matrix Calculus, With Applications, Ellis Horwood Ltd., England (1981)
##[3]
K. N. Murty, P. V. S. Lakshmi , On dichotomy and well-conditioning in two-point boundary value problems, Applied Mathematics and Computations , 38 (1990), 179-199
##[4]
M. S. N. Murty, B. V. Appa Rao, On conditioning for three-point boundary value problems, Indian Journal of Mathematics , 45 (2003), 211-221
##[5]
M. S. N. Murty, B. V. Appa Rao, On two point boundary value problems for :X = AX + XB, J. Ultra Scientist of Physical Sciences , 16 (2004), 223-227
##[6]
M. S. N. Murty, B. V. Appa Rao, G. Suresh Kumar, Controllability, observability and realizability of matrix Lyapunov systems, Bull. Korean. Math. Soc. , 43 (2006), 149-159
##[7]
M. S. N. Murty, G. Suresh Kumar, On dichotomy and conditioning for two-point boundary value problems associated with first order matrix Lyapunov systems, J. Korean Math. Soc. , 45 (2008), 1361-1378
]
A NEW REGULARITY CRITERION FOR THE NAVIER-STOKES EQUATIONS
A NEW REGULARITY CRITERION FOR THE NAVIER-STOKES EQUATIONS
en
en
We study the incompressible Navier-Stokes equations in the entire
three-dimensional space. We prove that if
\(\partial_3u_3 \in L^{s_1}_ t L^{r_1}_x\) and \(u_1u_2 \in L^{s_2}_ t L^{r_2}_x\),
then the solution is regular. Here
\(\frac{2}{s_1}+\frac{3}{r_1}\leq 1, 3\leq r_1\leq\infty,\frac{2}{s_2}+\frac{3}{r_2}\leq1\) and
\(3\leq r_2\leq\infty\).
126
129
HU
YUE
School of Mathematics and Information Science
Henan Polytechnic University
China
huu3y2@163.com
WU-MING
LI
School of Mathematics and Information Science
Henan Polytechnic University
China
liwum0626@126.com
Navier-Stokes equations
Leray-Hopf weak solution
Regularity.
Article.4.pdf
[
[1]
J. Leray , Sur le mouvement d'un liquide visqueux emplissant l'espace, Acta Math. , 63 (1934), 193-248
##[2]
D. Chae, J. Lee, Regularity criterion in terms of pressure for the Navier-Stokes equations, Nonlinear Anal.TMA , 46 (2001), 727-735
##[3]
I. Kukavica, M. Ziane, Navier-Stokes equations with regularity in one direction, J. Math. Phys. 48, Art. ID 065203. (2007)
##[4]
J. Serrin, On the interior regularity of weak solutions of the Navier-Stokes equations, Arch. Ration. Mech. Anal. , 9 (1962), 187-195
##[5]
L. Escauriaza, G. Seregin, V. Sverk, On backward uniqueness for parabolic equations, Zap. Nauch. Seminarov POMI , 288 (2002), 100-103
]
PROOFS OF THREE OPEN INEQUALITIES WITH POWER-EXPONENTIAL FUNCTIONS
PROOFS OF THREE OPEN INEQUALITIES WITH POWER-EXPONENTIAL FUNCTIONS
en
en
The main aim of this paper is to give a complete proof to the open
inequality with power-exponential functions
\[a^{ea} + b^{eb} \geq a^{eb} + b^{ea},\]
which holds for all positive real numbers a and b. Notice that this inequality
was proved in [1] for only
\(a \geq b \geq \frac{1}{ e}\) and \(\frac{1}{ e} \geq a \geq b\).In addition, other two
open inequalities with power-exponential functions are proved, and three new
conjectures are presented.
130
137
VASILE
CIRTOAJE
Department of Automatic Control and Computers
University of Ploiesti
Romania
vcirtoaje@upg-ploiesti.ro
Open inequality
Power-exponential function
AM-GM inequality.
Article.5.pdf
[
[1]
V. Cirtoaje, On some inequalities with power-exponential functions, J. Ineq. Pure Appl. Math., 10 (1), Art. 21, [http://www.emis.de/journals/JIPAM/article 1077.html?sid=1077]. (2009)
##[2]
V. Cirtoaje , Art of Problem Solving Forum, [http://www.artofproblemsolving. com/Forum/viewtopic.php?t=327116]. , (2010)
##[3]
V. Cirtoaje, A. Zeikii , Art of Problem Solving Forum, [http:// www.artofproblemsolving.com/Forum/viewtopic.php?t=118722]., (2006)
##[4]
L. Matejicka, Solution of one conjecture on inequalities with power-exponential functions, J. Ineq. Pure Appl. Math., 10 (3), [http://www. emis.de/journals/JIPAM/article1128.html?sid=1128]. (2009)
]
EXISTENCE RESULTS FOR IMPULSIVE SYSTEMS WITH NONLOCAL CONDITIONS IN BANACH SPACES
EXISTENCE RESULTS FOR IMPULSIVE SYSTEMS WITH NONLOCAL CONDITIONS IN BANACH SPACES
en
en
According to semigroup theories and Sadovskii fixed point theorem, this paper is mainly concerned with the existence of solutions for an
impulsive neutral differential and integrodifferential systems with nonlocal conditions in Banach spaces. As an application of this main theorem, a practical
consequence is derived for the sub-linear growth case. In the end, an example
is also given to show the application of our result.
138
151
V.
KAVITHA
Department of Mathematics
Karunya University, ,
India
M. MALLIKA
ARJUNAN
Department of Mathematics
Karunya University
India
arjunphd07@yahoo.co.in
C.
RAVICHANDRAN
Department of Mathematics
Karunya University
India
Nonlocal condition
Impulsive differential equation
Sadovskii fixed point theorem
Article.6.pdf
[
[1]
H. Akca, A. Boucherif, V. Covachev , Impulsive functional differential equations with nonlocal conditions, Inter. J. Math. Math. Sci., 29(5) (2002), 251-256
##[2]
A. Anguraj, K. Karthikeyan, Existence of solutions for impulsive neutral functional differential equations with nonlocal conditions, Nonlinear Anal., 70(7) (2009), 2717-2721
##[3]
L. Byszewski, Theorems about the existence and uniqueness of a solution of a semilinear evolution nonlocal Cauchy problem, J. Math. Anal. Appl., 162 (1991), 496-505
##[4]
L. Byszewski, V. Lakshmikantham, Theorems about existence and uniqueness of a solution of a nonlocal abstract Cauchy problem in a Banach space, Appl. Anal., 40 (1990), 11-19
##[5]
Y.-K. Chang, V. Kavitha, M. Mallika Arjunan, Existence results for impulsive neutral differential and integrodifferential equations with nonlocal conditions via fractional operators, Nonlinear Analysis: Hybrid Systems, 4 (2010), 32-43
##[6]
Y.-K. Chang, A. Anguraj, M. Mallika Arjunan, Existence results for non-densely defined neutral impulsive differential inclusions with nonlocal conditions, J. Appl. Math. Comput., 28(1) (2008), 79-91
##[7]
K. Deimling, Multivalued Differential Equations, de Gruyter, Berlin (1992)
##[8]
K. Deng, Exponential decay of solutions of semilinear parabolic equations with nonlocal initial conditions, J. Math. Anal. Appl., 179 (1993), 630-637
##[9]
K. Ezzinbi, X. Fu, K. Hilal, Existence and regularity in the \(\alpha\)-norm for some neutral partial differential equations with nonlocal conditions, Nonlinear Anal., 67 (2007), 1613-1622
##[10]
X. Fu, K. Ezzinbi, Existence of solutions for neutral functional differential evolutions equations with nonlocal conditions, Nonlinear Anal., 54 (2003), 215-227
##[11]
E. Hernández, H. R. Henriquez, Impulsive partial neutral differential equations, Appl. Math. Lett., 19 (3) (2006), 215-222
##[12]
E. Hernández, H. R. Henriquez, R. Marco, Existence of solutions for a class of impulsive partial neutral functional differential equations, J. Math. Anal. Appl., 331 (2) (2007), 1135-1158
##[13]
S. Hu, N. Papageorgiou, Handbook of Multivalued Analysis, Volume 1: Theory, Kluwer, Dordrecht, Boston, London (1997)
##[14]
V. Lakshmikantham, D. D. Bainov, P. S. Simeonov, Theory of Impulsive Differential Equations, World Scientific, Singapore (1989)
##[15]
J. H. Liu, Nonlinear impulsive evolution equations, Dynam. Contin. Discrete Impuls. Systems, 6 (1) (1999), 77-85
##[16]
A. Pazy, Semigroups of linear operators and applications to partial differential equations, Springer-Verlag, Newyork (1983)
##[17]
Y. V. Rogovchenko, Impulsive evolution systems: main results and new trends, Dynam. Contin. Discrete Impuls. Systems, 3 (1) (1997), 57-88
##[18]
Y. V. Rogovchenko, Nonlinear impulse evolution systems and applications to population models, J. Math. Anal. Appl., 207 (2) (1997), 300-315
##[19]
B. N. Sadovskii , On a fixed point principle, Functional Analysis and Applications, 1(2) (1967), 74-76
##[20]
A. M. Samoilenko, N. A. Perestyuk, Impulsive Differential Equations, World Scientific, Singapore (1995)
##[21]
V. kavitha, M. Mallika Arjunan, Controllability of non-densely defined impulsive neutral functional differential systems with infinite delay in Banach spaces, Nonlinear Analysis: Hybrid Systems, 4(3) (2010), 441-450
]
CONTROLLABILITY OF IMPULSIVE QUASI-LINEAR FRACTIONAL MIXED VOLTERRA-FREDHOLM-TYPE INTEGRODIFFERENTIAL EQUATIONS IN BANACH SPACES
CONTROLLABILITY OF IMPULSIVE QUASI-LINEAR FRACTIONAL MIXED VOLTERRA-FREDHOLM-TYPE INTEGRODIFFERENTIAL EQUATIONS IN BANACH SPACES
en
en
In this paper, we establish a sufficient condition for the controllability of impulsive quasi-linear fractional mixed Volterra-Fredholm-type integrodifferential equations in Banach spaces. The results are obtained by using
Banach contraction fixed point theorem combined with the fractional calculus
theory.
152
169
V.
KAVITHA
Department of Mathematics
Karunya University
India
kavi_velubagyam@yahoo.co.in
M. MALLIKA
ARJUNAN
Department of Mathematics
Karunya University
India
arjunphd07@yahoo.co.in
controllability
quasi-linear differential equation
fractional calculus
nonlocal condition
integrodifferential equation
evolution equation
fixed point.
Article.7.pdf
[
[1]
R. P. Agarwal, M. Benchohra, B. A. Slimani, Existence results for differential equations with fractional order impulses, Memoirs on Differential Equations and Mathematical Physics, 44 (2008), 1-21
##[2]
R. P. Agarwal, M. Belmekki, M. Benchohra, A survey on semilinear differential equations and inclusions involving Riemann-Liouville fractional derivative, Advances in Difference Equations, Article ID 981728, 2009 (2009), 1-47
##[3]
R. P. Agarwal, M. Benchohra, S. Hamani, A survey on existence results for boundary value problems of nonlinear fractional differential equations and inclusions , Acta Appl. Math., 109(3) (2010), 973-1033
##[4]
R. P. Agarwal, Y. Zhou, Y. He, Existence of fractional neutral functional differential equations, Comp. Math. Appl., 59 (2010), 1095-1100
##[5]
B. Ahmad, S. Sivasundaram, Existence results for nonlinear impulsive hybrid boundary value problems involving fractional differential equations, Nonlinear Analysis: Hybrid Systems, 3(3) (2009), 251-258
##[6]
B. Ahmad, J. J. Nieto, Existence results for a coupled system of nonlinear fractional differential equations with three-point boundary conditions, Comp. Math. Appl, 58 (2009), 1838-1843
##[7]
B. Ahmad, J. J. Nieto, Existence results for nonlinear boundary value problems of fractional integrodifferential equations with integral boundary conditions, Article ID 708576., 2009 (2009), 1-11
##[8]
H. Amann, Quasilinear evolution equations and parabolic systems, Trans. Amer. Math. Soc., 29 (1986), 191-227
##[9]
D. Bahuguna, Quasilinear integrodifferential equations in Banach spaces, Nonlinear Anal., 24 (1995), 175-183
##[10]
Z. Bai, H. Lü, Positive solutions for boundary value problem of nonlinear fractional differential equations, J. Math. Anal. Appl., 311 (2005), 495-505
##[11]
K. Balachandran, K. Uchiyama, Existence of solutions of quasilinear integrodifferential equations with nonlocal condition, Tokyo. J. Math., 23 (2000), 203-210
##[12]
K. Balachandran, F. P. Samuel , Existence of solutions for quasilinear delay integrodifferential equations with nonlocal conditions, Electronic Journal of Differential Equations, 2009 (2009), 1-7
##[13]
K. Balachandran, F. P. Samuel, Existence of mild solutions for quasilinear integrodifferential equations with impulsive conditions, Electronic Journal of Differential Equations, 2009(84) (2009), 1-9
##[14]
K. Balachandran, J. Y. Park, S. H. Park, Controllability of nonlocal impulsive quasi- linear integrodifferential systems in Banach spaces, Reports on Mathematical Physics, 65(2) (2010), 247-257
##[15]
K. Balachandran, J. P. Dauer, Controllability of nonlinear systems in Banach spaces: a survey, J. Optim. Theory Appl., 115 (2002), 7-28
##[16]
K. Balachandran, J. H. Kim, Remarks on the paper ''Controllability of second order differential inclusion in Banach spaces[J. Math. Anal. Appl. 285, 537-550 (2003)]. , J. Math. Anal. Appl., 324 (2006), 746-749
##[17]
K. Balachandran, J. Y. Park, Controllability of fractional integrodifferential systems in Banach spaces, Nonlinear Analysis: Hybrid Systems, 3(4) (2009), 363-367
##[18]
K. Balachandran, S. Kiruthika, Existence of solutions of abstract fractional impulsive semilinear evolution equations, Electronic Journal of Qualitative Theory of Differential Equations, 2010(4) (2010), 1-12
##[19]
K. Balachandran, S. Kiruthika, J. J. Trujillo, Existence results for fractional impulsive integrodifferential equations in Banach spaces, Commun Nonlinear Sci Numer Simulat, doi:10.1016/j.cnsns.2010.08.005. (2010)
##[20]
M. Benchohra, B. A. Slimani , Existence and uniqueness of solutions to impulsive fractional differential equations, Electronic Journal of Differential Equations, 2009(10) (2009), 1-11
##[21]
M. Benchohra, J. Henderson, S. K. Ntouyas, A. Ouahab, Existence results for fractional functional differential inclusions with infinite delay and application to control theory, Fract. Calc. Appl. Anal., 11 (2008), 35-56
##[22]
M. Benchohra, J. Henderson, S. K. Ntouyas, Existence results for impulsive multivalued semilinear neutral functional inclusions in Banach spaces, J. Math. Anal. Appl., 263 (2001), 763-780
##[23]
M. Benchohra, J. Henderson, S. K. Ntouyas, A. Ouahab, Existence results for fractional order functional differential equations with infinite delay, J. Math. Anal. Appl., 338 (2008), 1340-1350
##[24]
M. Benchohra, A. Ouahab, Controllability results for functional semilinear differential inclusions in Fréchet spaces, Nonlinear Anal., 61 (2005), 405-423
##[25]
B. Bonila, M. Rivero, L. Rodriquez-Germa, J. J. Trujilio, Fractional differential equations as alternative models to nonlinear differential equations, Appl. Math. Comput., 187 (2007), 79-88
##[26]
L. Byszewski , Theorems about existence and uniqueness of solutions of solutions of a semi- linear evolution nonlocal Cauchy problem, J. Math. Anal. Appl., 162 (1991), 494-505
##[27]
L. Byszewski, V. Lakshmikantham, Theorem about the existence and uniqueness of a solution of a nonlocal abstract Cauchy problem in a Banach space, Appl. Anal., 40 (1991), 11-19
##[28]
M. Chandrasekaran, Nonlocal Cauchy problem for quasilinear integrodifferential equations in Banach spaces, Electronic Journal of Differential Equations, 2007(33) (2007), 1-6
##[29]
Y. K. Chang, J. J. Nieto, Some new existence results for fractional differential inclusions with boundary conditions, Math. Comput. Modelling, 49 (2009), 605-609
##[30]
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]
ON A CERTAIN CLASS OF HARMONIC MULTIVALENT FUNCTIONS
ON A CERTAIN CLASS OF HARMONIC MULTIVALENT FUNCTIONS
en
en
The purpose of the present paper is to study some results involving coefficient conditions, extreme points, distortion bounds, convolution
conditions and convex combination for a new class of harmonic multivalent
functions in the open unit disc. Relevant connections of the results presented
here with various known results are briefly indicated.
170
179
SAURABH
PORWAL
Department of Mathematics
Janta College
India
POONAM
DIXIT
Department of Mathematics
Christ Church College
India
saurabhjcb@rediffmail.com
VINOD
KUMAR
Department of Mathematics
Christ Church College
India
Harmonic
Univalent
Multivalent functions
Fractional calculus.
Article.8.pdf
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