]>
2015
8
1
ISSN 2008-1898
84
Stability of derivations in fuzzy normed algebras
Stability of derivations in fuzzy normed algebras
en
en
In this paper, we find a fuzzy approximation of derivation for an m-variable additive functional equation. In
fact, using the fixed point method, we prove the Hyers-Ulam stability of derivations on fuzzy Lie \(C^*\)-algebras
for the the following additive functional equation
\[\Sigma^m _{i=1} f ( mx_i + \Sigma^m _{j=1, j\neq i} x_j ) + f (\Sigma^m _{i=1} x_i ) = 2f (\Sigma^m_{ i=1} mx_i )\]
for a given integer m with \(m \geq 2\).
1
7
Yeol Je
Cho
Department of Mathematics Education and the RINS
Gyeongsang National University
Korea
yjcho@gnu.ac.kr
Choonkill
Park
Research Institute for Natural Sciences
Hanyang University
Korea
baak@hanyang.ac.kr
Young-Oh
Yang
Department of Mathematics
Jeju National University
Korea
yangyo@jejunu.ac.kr
Fuzzy normed space
additive functional equation
fixed point
derivation
\(C^*\)-algebra
Lie \(C^*\)-algebra
Hyers-Ulam stability.
Article.1.pdf
[
[1]
R. P. Agarwal, Y. J. Cho, R. Saadati, S. Wang, Nonlinear L-fuzzy stability of cubic functional equations, J. Inequal. Appl., 2012 (2012), 1-19
##[2]
L. Cădariu, V. Radu, Fixed points and the stability of Jensen's functional equation, J. Inequal. Pure Appl. Math., 4, no. 1, Art. 4 (2003)
##[3]
J. Diaz, B. Margolis, A fixed point theorem of the alternative for contractions on a generalized complete metric space, Bull. Amer. Math. Soc., 74 (1968), 305-309
##[4]
C. Park, S. Y. Jang, R. Saadati, Fuzzy approximate of homomorphisms, J. Comput. Anal. Appl., 14 (2012), 833-841
##[5]
C. Park, M. Eshaghi Gordji, R. Saadati, Random homomorphisms and random derivations in random normed algebras via fixed point method, J. Inequal. Appl., 2012 (2012), 1-13
##[6]
R. Saadati, S. M. Vaezpour, Some results on fuzzy Banach spaces, J. Appl. Math. Comput., 17 (2005), 475-484
##[7]
R. Saadati, C. Park, Non-Archimedian L-fuzzy normed spaces and stability of functional equations, Comput. Math. Appl., 60 (2010), 2488-2496
##[8]
R. Saadati, On the , J. Comput. Anal. Appl., 14 (2012), 996-999
##[9]
S. M. Ulam, A Collection of the Mathematical Problems, Interscience Publ., New York (1960)
##[10]
G. Zamani-Eskandani , On the Hyers-Ulam-Rassias stability of an additive functional equation in quasi-Banach spaces , J. Math. Anal. Appl., 345 (2008), 405-409
]
Some common coupled fixed point theorems for generalized contraction in \(b\)-metric spaces
Some common coupled fixed point theorems for generalized contraction in \(b\)-metric spaces
en
en
The aim of this paper is to prove the existence and uniqueness of a common coupled fixed point for a pair of
mappings in a complete \(b\)-metric space in view of diverse contractive conditions. In addition, as a bi-product
we obtain several new common coupled fixed point theorems.
8
16
Nidhi
Malhotra
Department of Mathematics, Hindu College
University of Delhi
India
nidmal25@gmail.com
Bindu
Bansal
Department of Mathematics, Hindu College
University of Delhi
India
bindubansaldu@gmail.com
Common fixed point
coupled fixed point
coupled coincidence point
contractive mappings
b-metric spaces.
Article.2.pdf
[
[1]
M. Akkouchi, A common fixed point theorem for expansive mappings under strict implicit conditions on b-metric spaces, Acta Univ. Palack. Olomuc. Fac. Rerum Natur. Math., 50 (2011), 5-15
##[2]
H. Aydi, M. F. Bota, E. Karapinar, S. Mitrović, A fixed point theorem for set-valued quasi-contractions in b-metric spaces, Fixed Point Theory Appl., 2012 (2012), 1-8
##[3]
I. A. Bakhtin, The contraction mapping principle in quasimetric spaces, Functional Analysis, 30 (1989), 26-37
##[4]
M. Boriceanu, Fixed point theory for multivalued generalized contraction on a set with two b-metrics, Studia Univ. Babes-Bolyai Math., 3 (2009), 1-14
##[5]
S. Czerwik , Contraction mappings in b-metric spaces, Acta Math. Inform. Univ. Ostraviensis, 1 (1993), 5-11
##[6]
T. Gnana Bhaskar, V. Lakshmikantham, Fixed point theorems in partially ordered metric spaces and applications, Nonlinear Analysis: TMA, 65 (2006), 1379-1393
##[7]
N. Hussain, D. Dorić, Z. Kadelburg, S. Radenović , Suzuki-type fixed point results in metric type spaces, Fixed Point Theory Appl., 2012 (2012), 1-12
##[8]
M. Jovanović, Z. Kadelburg, S. Radenović, Common fixed point results in metric-type spaces, Fixed Point Theory Appl., 2010 (2010), 1-15
##[9]
M. Kir, H. Kiziltunc, On some well known fixed point theorems in b-metric spaces, Turkish J. Anal. Number Theory, 1 (2013), 13-16
##[10]
M. O. Olatinwo, C. O. Imoru, A generalization of some results on multi-valued weakly Picard mappings in b-metric space, Fasciculi Mathematici, 40 (2008), 45-56
##[11]
M. Păcurar , A fixed point result for \(\phi\)-contractions on b- metric spaces without the boundedness assumption , Fasc. Math., 43 (2010), 127-137
]
Singular values and fixed points of family of generating function of Bernoullis numbers
Singular values and fixed points of family of generating function of Bernoullis numbers
en
en
Singular values and fixed points of one parameter family of generating function of Bernoulli's numbers,
\(g_\lambda(z) = \lambda\frac{z}{e^z-1} , \lambda\in \mathbb{R}-\{0\}\), are investigated. It is shown that the function \(g_\lambda(z)\) has infinitely many singular
values and its critical values lie outside the open disk centered at origin and having radius \(\lambda\). Further,
the real fixed points of \(g_\lambda(z)\) and their nature are determined. The results found are compared with the
functions \(\lambda\tan z, E_\lambda(z) = \lambda \frac{e^z-1}{z}\) and\( f_\lambda(z) = \lambda \frac{z}{z+4}e^z\) for \(\lambda > 0\).
17
22
Mohammad
Sajid
College of Engineering
Qassim University
Saudi Arabia
msajid@qec.edu.sa
Fixed points
critical values
singular values.
Article.3.pdf
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[1]
A. F. Beardon , Iteration of Rational Functions, Springer, New York (1991)
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R. L. Devaney, L. Keen, Dynamics of meromorphic maps: Maps with polynomial Schwarzian derivative, Ann. Sci. Ec. Norm. Sup., 22 (1989), 55-79
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X. H. Hua, C. C. Yang, Dynamics of Transcendental Functions, Gordon and Breach Sci. Pub., Amsterdam (1998)
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S. Morosawa, Y. Nishimura, M. Taniguchi, T. Ueda, Holomorphic Dynamics, Cambridge University Press, Cambridge (2000)
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T. Nayak, M. Guru Prem Prasad, Iteration of certain meromorphic functions with unbounded singular values, Ergod. Th. Dynam. Sys., 30 (2010), 877-891
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M. Guru Prem Prasad, Chaotic burst in the dynamics of \(f_\lambda(z) = \lambda \frac{\sinh(z)}{ z}\), Regul. Chaotic Dyn., 10 (2005), 71-80
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M. Guru Prem Prasad , Tarakanta Nayak, Dynamics of certain class of critically bounded entire transcendental functions, J. Math. Anal. Appl., 329 (2007), 1446-1459
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G. Rottenfusser, J. Ruckert, L. Rempe, D. Schleicher, Dynamics rays of bounded-type entire functions, Ann. Math., 173 (2011), 77-125
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M. Sajid, G. P. Kapoor, Dynamics of a family of non-critically finite even transcendental meromorphic functions, Regul Chaotic Dyn., 9 (2004), 143-162
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M. Sajid , Real and complex dynamics of one parameter family of meromorphic functions, Far East J. Dynamical Sys., 19 (2012), 89-105
##[13]
J. Zheng, Singular Values of Meromorphic Functions, Value Distribution of Meromorphic Functions, Springer, (2011), 229-266
]
Integrability and \(L^1\)-convergence of fuzzy trigonometric series with special fuzzy coefficients
Integrability and \(L^1\)-convergence of fuzzy trigonometric series with special fuzzy coefficients
en
en
In this paper, we generalize some classical results on the integrability of trigonometric series using the
notion of integrability in fuzzy \(L^1\)-norm. Here, we introduce new classes of fuzzy coefficients and obtain
the necessary and sufficient conditions for \(L^1\)-convergence of fuzzy trigonometric series. Also, an example
is given for the existence of new classes of fuzzy coefficients.
23
39
Sandeep
Kaur
School of Mathematics and Computer Applications
Thapar University Patiala
India
sandeepchouhan247@gmail.com
Jatinderdeep
Kaur
School of Mathematics and Computer Applications
Thapar University Patiala
India
jkaur@thapar.edu
Fuzzy numbers
fuzzy trigonometric series
integrability
convergence in fuzzy \(L^1\)-norm.
Article.4.pdf
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M. Stojaković, Z. Stojaković, Series of fuzzy sets, Fuzzy Sets and Systems, 160 (2009), 3115-3127
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Ö. Talo, F. Başar, On the space bvp(F) of sequences of p-bounded variation of fuzzy numbers, Acta Math. Sin. Eng. Ser., 24 (2008), 965-972
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Ö. Talo, F. Başar, Determination of the duals of classical sets of sequences of fuzzy numbers and related matrix transformations, Comput. Math. Appl., 58 (2009), 717-733
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M. Z. Wang, S. P. Zhou, Applications of MVBV condition in \(L^1\) integrability, Acta. Math. Hungar, 129 (2010), 70-80
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]
Applications of discriminant analysis on shear turbulence data in wavenumber domain
Applications of discriminant analysis on shear turbulence data in wavenumber domain
en
en
This paper proposed a discriminant analysis method to realize the auto matching of shear spectra and
improve the precision of the shear turbulence data. The discriminant analysis method includes two parts,
firstly, in order to eliminate noise data, cross validation method is used to data preprocessing, and secondly,
maximum likelihood method is used to get discriminant function to realize the auto matching of the spectra.
South China Sea experiment is used to verify the validity of the method.
40
45
Yongfang
Wang
School of Informatics
Linyi University
P. R. China
greenworld6@163.com
Xin
Luan
College of Information Science & Engineering
Ocean University of China
P. R. China
luanxin@qingdao.gov.cn
Tongxing
Li
School of Informatics
Linyi University
P. R. China
litongx2007@163.com
Discriminant analysis
cross validation
data preprocessing
maximum likelihood.
Article.5.pdf
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[1]
George E. P. Box, George C. Tiao, Bayesian Inference in Statistical Analysis, John Wiley & Sons, Inc., (1992)
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H. Dong, S. E. Dosso, Bayesian inversion of interface-wave dispersion for seabed shear-wave speed profiles, IEEE Journal of Oceanic Engineering, 36 (2011), 1-11
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G. J. McLachlan, Discriminant Analysis and Statistical Pattern Recognition, John Wiley & Sons, Inc., (1992)
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S. Mika, G. Rätsch, J. Weston, B. Schölkopf, K.-R. Müller, Fisher discriminant analysis with kernels, Neural networks for signal processing IX, Processing of the 1999 IEEE Signal Processing Society Workshop, (1999), 41-48
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X.-H. Xie, X.-D. Shang, G.-Y. Shang, L. Sun, Variations of diurnal and inertial spectral peaks near the bi-diurnal critical latitude, Geophysical Research Letters, 36 (2009), 1-02606
]
On \(\nabla^{**}\)-distance and fixed point theorems in generalized partially ordered \(D^*\)-metric spaces
On \(\nabla^{**}\)-distance and fixed point theorems in generalized partially ordered \(D^*\)-metric spaces
en
en
In this paper, we introduce a new concept on a complete generalized \(D^*\)-metric space by using the concept
of generalized \(D^*\)-metric space (\(D^*\)-cone metric space) called \(\nabla^{**}\)-distance and, by using the concept of the
\(\nabla^{**}\)-distance we prove some new fixed point theorems in complete partially ordered generalized \(D^*\)-metric
space which is the main result of our paper.
46
54
Alaa Mahmood AL.
Jumaili
School of Mathematics and Statistics
Huazhong University of Science and Technology Wuhan city
China
alaa_mf1970@yahoo.com
Xiao Song
Yang
School of Mathematics and Statistics
Huazhong University of Science and Technology Wuhan city
China
yangxs@cqupt.edu.cn
Fixed point theorem
generalized \(D^*\)-metric spaces
\(\nabla^{**}\)-distance.
Article.6.pdf
[
[1]
R. P. Agarwal, M. A. El-Gebeily, D. O'Regan, Generalized contractions in partially ordered metric spaces , Appl. Anal., 87 (2008), 1-8
##[2]
C. T. Aage, J. N. Salunke, Some fixed points theorems in generalized \(D^*\)-metric spaces, Appl. Sci., 12 (2010), 1-13
##[3]
A. M. AL. Jumaili, X. S. Yang, Fixed point theorems and \(\nabla^{**}\)-distance in partially ordered \(D^*\)-metric spaces, Int. J. Math. Anal., 6 (2012), 2949-2955
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L. B. Ćirić, A generalization of Banach's contraction principle, Proc. Amer. Math. Soc., 45 (1974), 267-273
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L. B. Ćirić, Coincidence and fixed points for maps on topological spaces, Topology Appl., 154 (2007), 3100-3106
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J. X. Fang, Y. Gao , Common fixed point theorems under strict contractive conditions in Menger spaces, Nonlinear Anal.-TMA., 70 (2009), 184-193
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T. Gnana Bhaskar, V. Lakshmikantham, Fixed point theorems in partially ordered metric spaces and applications, Nonlinear Anal.-TMA., 65 (2006), 1379-1393
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T. Gnana Bhaskar, V. Lakshmikantham, J. Vasundhara Devi, Monotone iterative technique for functional differential equations with retardation and anticipation, Nonlinear Anal.-TMA., 66 (2007), 2237-2242
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N. Hussain, Common fixed points in best approximation for Banach operator pairs with Ćirić type I-contractions, J. Math. Anal. Appl., 338 (2008), 1351-1363
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J. J. Nieto, R. R. Lopez, Contractive mapping theorems in partially ordered sets and applications to ordinary differential equations, Order, 22 (2005), 223-239
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V. L. Nguyen, X. T. Nguyen, Common fixed point theorem in compact \(D^*\)-metric spaces, Int. Math. Forum, 6 (2011), 605-612
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J. J. Nieto, R. R. Lopez, Existence and uniqueness of fixed point in partially ordered sets and applications to ordinary differential equations, Acta Math. Sin. Eng. Ser., 23 (2007), 2205-2212
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A. Petruşel, I. A. Rus, Fixed point theorems in ordered L-spaces, Proc. Amer. Math. Soc., 134 (2006), 411-418
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A. C. M. Ran, M. C. B. Reurings, A fixed point theorem in partially ordered sets and some applications to matrix equations , Proc. Amer. Math. Soc., 132 (2004), 1435-1443
##[18]
S. Sedghi, N. Shobe, H. Zhou, A common fixed point theorem in \(D^*\)-metric spaces, Fixed Point Theory and Applications. Article ID 27906, (2007), 1-13
##[19]
R. Saadati, S. M. Vaezpour, P. Vetro, B. E. Rhoades, Fixed point theorems in generalized partially ordered G-metric spaces, Mathematical and Computer Modelling, 52 (2010), 797-801
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T. Veerapandi, A. M. Pillai, Some common fixed point theorems in \(D^*\)- metric spaces , African J. Math. Computer Sci. Research, 4 (2011), 357-367
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T. Veerapandi, A. M. Pillai, A common fixed point theorems in \(D^*\)- metric spaces, African J. Math. Computer Sci. Research, 4 (8) (2011), 273-280
]
Fuzzy fixed point theorems for multivalued fuzzy contractions in \(b\)-metric spaces
Fuzzy fixed point theorems for multivalued fuzzy contractions in \(b\)-metric spaces
en
en
In this paper, we introduce the new concept of multivalued fuzzy contraction mappings in \(b\)-metric spaces
and establish the existence of \(\alpha\)-fuzzy fixed point theorems in \(b\)-metric spaces which can be utilized to derive
Nadler's fixed point theorem in the framework of b-metric spaces. Moreover, we provide examples to support
our main result.
55
63
Supak
Phiangsungnoen
Department of Mathematics, Faculty of Science
Centre of Excellence in Mathematics
King Mongkut's University of Technology Thonburi
Thailand
Thailand
supuk_piang@hotmail.com
Poom
Kumam
Department of Mathematics, Faculty of Science
Centre of Excellence in Mathematics
King Mongkut's University of Technology Thonburi
Thailand
Thailand
poom.kum@kmutt.ac.th
\(b\)-metric spaces
fuzzy fixed point
fuzzy mappings
fuzzy set.
Article.7.pdf
[
[1]
M. Abbas, B. Damjanović, R. Lazović, Fuzzy common fixed point theorems for generalized contractive mappings, Appl. Math. Lett., 23 (2010), 1326-1330
##[2]
J. Ahmad, A. Azam, S. Romaguera , On locally contractive fuzzy set valued mappings, J. Inequalities Appl., 2014 (2014), 1-10
##[3]
H. Aydi, M-F. Bota, E. Karapinar, S. Mitrović, A fixed point theorem for set-valued quasi-contractions in b-metric spaces, Fixed Point Theory Appl, 2012 (2012), 1-8
##[4]
H. Aydi, M-F. Bota, E. Karapinar, S. Moradi , A common fixed point for weak -contractions on b-metric spaces, Fixed Point Theory, 13 (2012), 337-346
##[5]
A. Azam, M. Arshad, I. Beg, Fixed points of fuzzy contractive and fuzzy locally contractive maps, Chaos, Solitons and Fractals, 4 (2009), 2836-2841
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A. Azam, I. Beg, Common fixed points of fuzzy maps, Mathematical and Computer Modelling, 49 (2009), 1331-1336
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I. A. Bakhtin, The contraction mapping principle in quasimetric spaces , Funct. Anal., Unianowsk Gos. Ped. Inst., 30 (1989), 26-37
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V. Berinde , Generalized contractions in quasimetric spaces, Seminar on Fixed Point Theory, Preprint, 3 (1993), 3-9
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M. Boriceanu, M. Bota, A.Petru, Multivalued fractals in b-metric spaces , Central European J. Math., 8 (2010), 367-377
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M. Boriceanu, A. Petruşel, I. A. Rus , Fixed point theorems for some multivalued generalized contractions in b-metric spaces, Int. J. Math. Stat., 6 (2010), 65-76
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M. Boriceanu, Strict fixed point theorems for multivalued operators in b-metric spaces, Int. J. Mod. Math., 4 (2009), 285-301
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M. Boriceanu , Fixed point theory for multivalued generalized contraction on a set with two b-metrics, Studia Univ. Babeş-Bolyai, Mathematica, 3 (2009), 3-14
##[13]
R. K. Bose, M. K. Roychowdhury, Fixed point theorems for generalized weakly contractive mappings, Surv. Math. Appl., 4 (2009), 215-238
##[14]
M. Bota, E. Karapnar, O.Mleşniţe, Ulam-Hyers stability results for fixed point problems via \(\alpha-\psi\) -contractive mapping in (b)-metric space, Abstract and Applied Analysis, Article ID 825293 , 2013 (2013), 1-6
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S. Czerwik, Contraction meppings in b-metric spaces, Acta Mathematica et Informatica Universitatis Ostraviensis, 1 (1993), 5-11
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S. Czerwik, K. Dlutek, S. L. Singh, Round-off stability of iteration procedures for operators in b-metric spaces, J. Natur. Phys. Sci., 11 (1997), 87-94
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S. Czerwik, Nonlinear set-valued contraction mappings in b-metric spaces, Atti Sem. Mat. Univ. Modena, 46 (1998), 263-276
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V. D. Estruch, A. Vidal , A note on fixed fuzzy points for fuzzy mappings, Rend Istit Univ Trieste, 32 (2001), 39-45
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M. Frigon, D. O'Regan, Fuzzy contractive maps and fuzzy fixed points, Fuzzy Sets and Systems, 129 (2002), 39-45
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M. A. Kutbi, J. Ahmad, A. Azam, N. Hussain, On fuzzy fixed points for fuzzy maps with generalized weak property, J. Appl. Math., Article ID 549504, 2014 (2014), 1-12
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M. A. Kutbi, E. Karapinar, J. Ahmad, A. Azam, Some fixed point results for multi-valued mappings in b-metric spaces, J. Inequalities Appl., 2014 (2014), 1-11
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Stability of an ACQ-functional equation in various matrix normed spaces
Stability of an ACQ-functional equation in various matrix normed spaces
en
en
Using the direct method and the fixed point method, we prove the Hyers-Ulam stability of the following
additive-cubic-quartic (ACQ ) functional equation
\[11[f(x + 2y) + f(x - 2y)]
= 44[f(x + y) + f(x - y)] + 12f(3y) - 48f(2y) + 60f(y) - 66f(x)\]
in matrix Banach spaces. Furthermore, using the fixed point method, we also prove the Hyers-Ulam stability
of the above functional equation in matrix fuzzy normed spaces.
64
85
Zhihua
Wang
School of Science
Hubei University of Technology
P. R. China
matwzh2000@126.com
Prasanna K.
Sahoo
Department of Mathematics
University of Louisville
USA
sahoo@louisville.edu
Fixed point method
Hyers-Ulam stability
matrix Banach space
matrix fuzzy normed space
additive-cubic-quartic functional equation.
Article.8.pdf
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