]>
2011
4
4
ISSN 2008-1898
123
\(L_p\)--Approximation by a Linear Combination of Summation-integral Type Operators
\(L_p\)--Approximation by a Linear Combination of Summation-integral Type Operators
en
en
The present paper is a study of some direct results in \(L_p\)−approximation
by a linear combination of summation-integral type operators. We obtain an
error estimate in terms of the higher order modulus of smoothness using some
properties of the Steklov mean.
218
235
Karunesh Kumar
Singh
Department of Mathematics
I. I. T. Roorkee
India
kksiitr.singh@gmail.com
P. N.
Agrawal
Department of Mathematics
I. I. T. Roorkee
India
pnappfma@gmail.com
Linear positive operators
linear combination
Steklov means
integral modulus of smoothness.
Article.1.pdf
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]
Existence, Uniqueness and Stability Results of Impulsive Stochastic Semilinear Functional Differential Equations with Infinite Delays
Existence, Uniqueness and Stability Results of Impulsive Stochastic Semilinear Functional Differential Equations with Infinite Delays
en
en
This article presents the results on existence, uniqueness and stability
of mild solution for impulsive stochastic semilinear functional differential
equations with non-Lipschitz condition and Lipschitz condition. The results
are obtained by using the method of successive approximation and Bihari’s
inequality.
236
246
A.
Vinodkumar
Department of Mathematics and Computer Applications
PSG College of Technology
India
vinod026@gmail.com
Existence
Uniqueness
Stability
Successive approximation
Bihari’s inequality.
Article.2.pdf
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]
Solvability of a nonlinear boundary value problem
Solvability of a nonlinear boundary value problem
en
en
In this paper we consider three point boundary value problems
of second order. We introduce new and sufficient conditions that allow us to
obtain the existence of a nontrivial solution by using Leray Schauder nonlinear
alternative. As an application, we give some examples to illustrate our results.
247
261
A.
Guezane-Lakoud
Laboratory of Advanced Materials, Faculty of Sciences
Badji Mokhtar University
Algeria
a_guezane@yahoo.fr
S.
KELAIAIA
Laboratory of Advanced Materials, Faculty of Sciences
Badji Mokhtar University
Algeria
kelaiaiasmail@yahoo.fr
Fixed point theorem
Three point boundary value problem
Non trivial solution.
Article.3.pdf
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R. Ma, Existence theorems for second order three-point boundary value problems, J. Math. Anal. Appl., 212 (1997), 545-555
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L. Shuhong, Y-P. Sun, Nontrivial solution of a nonlinear second order three point boundary value problem, Appl. Math. J., 22 (1) (2007), 37-47
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S. Sivasankaran, M. Mallika Arjunan, V. Vijayakumar, Existence of global solutions for impulsive functional differential equations with nonlocal conditions , J. Nonlinear. Sci. Appl., 4 (2) (2011), 102-114
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Y-P. Sun, Nontrivial solution for a three-point boundary-value problem, EJDE, 111 (2004), 1-10
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J. R. L. Webb, Optimal constants in a nonlocal boundary value problem, Nonlinear Anal., 63 (2005), 672-685
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F. Zhang, Multiple positive solution for nonlinear singular third order boundary value problem in abstract spaces, J. Nonlinear. Sci. Appl. , 1 (1) (2008), 36-44
]
Triple solutions for nonlinear singular m-point boundary value problem
Triple solutions for nonlinear singular m-point boundary value problem
en
en
In this paper, we study the existence of three solutions to the
following nonlinear m-point boundary value problem
\[
\begin{cases}
u''(t) + \beta^2u(t) = h(t)f(t, u(t)),\,\,\,\,\, 0 < t < 1,\\
u'(0) = 0, u(1) =\Sigma^{m-2}_{i=1}\alpha_i u(\eta_i),
\end{cases}
\]
where \(0<\beta<\frac{\pi}{2}, f\in C([0,1]\times \mathbb{R}^+, \mathbb{R}^+). h(t)\) is allowed to be singular at
\(t = 0\) and \(t = 1\). The arguments are based only upon the Leggett-Williams
fixed point theorem. We also prove nonexist results.
262
269
Fuli
Wang
School of Mathematics and Physics
Changzhou University
China
fuliwang2011@163.com
m-point boundary value problem
Positive solutions
Fixed point theorem.
Article.4.pdf
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##[9]
F. Wang, Y. Cui, F. Zhang, Existence of nonnegative solutions for second order m-point boundary value problems at resonance, Appl. Math. Comput. , 217 (2011), 4849-4855
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]
T-rough Semiprime Ideals on Commutative Rings
T-rough Semiprime Ideals on Commutative Rings
en
en
Rough sets were originally proposed in the presence of an equivalence
relation. An equivalence relation is sometimes difficult to be obtained in
rearward problems due to the vagueness and incompleteness of human knowledge.
The purpose of this paper is to introduce and discuss the concept of
T-rough semiprime ideal, T-rough fuzzy semiprime ideal and T-rough quotient
ideal in a commutative ring which are a generalization of rough set and approximation
theory. We compare relation between a rough ideal and a T-rough
ideal and prove some theorems.
270
280
S. B.
Hosseini
Department of Mathematics
Islamic Azad University, Sari Branch
Iran
sbhosseini@iausari.ac.ir
approximation space
rough ideal
semiprime ideal
T-rough set
set-valued homomorphism
T-rough semiprime ideal
T-rough fuzzy ideal
commutative ring.
Article.5.pdf
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]
Controllability of nonlocal impulsive functional integrodifferential evolution systems
Controllability of nonlocal impulsive functional integrodifferential evolution systems
en
en
In this paper, we establish a set of sufficient conditions for the controllability
of nonlocal impulsive functional integrodifferential evolution systems with finite delay. The
controllability results are obtained with out assuming the compactness condition on the
evolution operator by using the semigroup theory and applying the fixed point approach.
An example is provided to illustrate the theory.
281
291
B.
Radhakrishnan
Department of Mathematics
Bharathiar University
India
radhakrishnanb1985@gmail.com
K.
Balachandran
Department of Mathematics
Bharathiar University
India
kb.maths.bu@gmail.com
Controllability
impulsive integrodifferential system
evolution operator
fixed point theorem
nonlocal condition.
Article.6.pdf
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Y. K. Chang, Controllability of impulsive functional differential systems with infinite delay in Banach spaces, Chaos, Solitons and Fractals , 33 (2007), 1601-1609
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A. M. Samoilenko, N. A. Perestyuk, Impulsive Differential Equations, World Scientific, Singapore (1995)
##[22]
G. Xie, L. Wang, Controllability and observability of a class of linear impulsive systems , J. Math. Anal. Appl., 304 (2005), 336-355
]
Convergence of implicit random iteration process with errors for a finite family of asymptotically quasi-nonexpansive random operators
Convergence of implicit random iteration process with errors for a finite family of asymptotically quasi-nonexpansive random operators
en
en
In this paper, we prove that an implicit random iteration process with errors which is generated by a finite family of asymptotically quasi-
nonexpansive random operators converges strongly to a common random fixed
point of the random operators in uniformly convex Banach spaces.
292
307
GURUCHARAN SINGH
SALUJA
Department of Mathematics and Information Technology
Govt. Nagarjuna P.G. College of Science
India
saluja_1963@rediffmail.com
Asymptotically quasi nonexpansive random operator
common random fixed point
implicit random iteration scheme with errors
strong convergence
uniformly convex Banach space.
Article.7.pdf
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Exact Controllability of Semilinear Third Order Dispersion Equation
Exact Controllability of Semilinear Third Order Dispersion Equation
en
en
In this paper, a family of nonlinear functions is given for the exact
controllability of semilinear third order dispersion equation. The obtained
result has been illustrated by applying it on nonlinear Korteweg-de Vries (KdV)
equation.
308
314
N. K.
Tomar
Department of Mathematics
Indian Institute of Technology
India
nktomar@iitp.ac.ir
N.
Sukavanam
Department of Mathematics
Indian Institute of Technology
India
nsukvfma@iitr.ernet.ir
Exact controllability
Dispersion System
KdV Equation.
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]
STABILITY AND STABILIZATION OF IMPULSIVE AND SWITCHED HYBRID STOCHASTIC DELAY SYSTEMS
STABILITY AND STABILIZATION OF IMPULSIVE AND SWITCHED HYBRID STOCHASTIC DELAY SYSTEMS
en
en
Stability analysis is performed and stabilization strategies are proposed for a general class of stochastic delay differential equations subjected
to switching and impulses. Hybrid switching and impulses are combined to
exponentially stabilize an otherwise unstable stochastic delay system. Three
differential stabilization strategies are proposed, i.e. the average dwellime
approach, the impulsive stabilization, and a combined strategy. Both moment
stability and almost sure stability of the resulting impulsive and switched hybrid stochastic delay systems are investigated using the well-known Lyapunov-
Razumikhin method in the hybrid and stochastic setting. Several examples are
presented to illustrate the main results and numerical simulations are presented
to demonstrate the analytical results.
315
341
Jun
Liu
Department of Applied Mathematics
University of Waterloo
Canada
j49liu@uwaterloo.ca
Xinzhi
Liu
Department of Applied Mathematics
University of Waterloo
Canada
xzliu@uwaterloo.ca
Wei-Chau
Xie
Department of Civil and Environmental Engineering
University of Waterloo
Canada
xie@uwaterloo.ca
Switched system
impulsive system
hybrid system
delay system
stochastic system
exponential stability
impulsive stabilization
Lyapunov-Razumikhin method.
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