2012
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81
On the maximal ideal space of extended polynomial and rational uniform algebras
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Let K and X be compact plane sets such that K X. Let P(K)be the uniform closure of polynomials on K. Let R(K) be the closure of rationalfunctions K with poles o K. Dene P(X;K) and R(X;K) to be the uniformalgebras of functions in C(X) whose restriction to K belongs to P(K) and R(K),respectively. Let CZ(X;K) be the Banach algebra of functions f in C(X) suchthat fjK = 0. In this paper, we show that every nonzero complex homomorphism' on CZ(X;K) is an evaluation homomorphism ez for some z in XnK. By considering this fact, we characterize the maximal ideal space of the uniform algebraP(X;K). Moreover, we show that the uniform algebra R(X;K) is natural.
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1
12


S.
Moradi
Department of Mathematics, Faculty of Science, Arak University, Arak, 38156
88349, Iran.
Department of Mathematics, Faculty of Science,
Iran


T. G.
Honary
Faculty of Mathematical Sciences and Computer Engineering, Teacher Train
ing University, 599 Taleghani Avenue, Tehran, 15618, I.R. Iran.
Faculty of Mathematical Sciences and Computer
Iran


D.
Alimohammadi
Department of Mathematics, Faculty of Science, Arak University, Arak, 38156
88349, Iran.
Department of Mathematics, Faculty of Science,
Iran
Maximal ideal space
uniform algebras
nonzero complex homomorphism
Common fixed point theorems for occasionally weakly compatible mappings in Menger spaces and applications
2
2
In 2008, AlThaga and Shahzad [Generalized Inonexpansive selfmaps and invariant approximations, Acta Math. Sinica 24(5) (2008), 867{876]introduced the notion of occasionally weakly compatible mappings (shortly owcmaps) which is more general than all the commutativity concepts. In the presentpaper, we prove common xed point theorems for families of owc maps in Mengerspaces. As applications to our results, we obtain the corresponding xed pointtheorems in fuzzy metric spaces. Our results improve and extend the results ofKohli and Vashistha [Common xed point theorems in probabilistic metric spaces,Acta Math. Hungar. 115(12) (2007), 3747], Vasuki [Common xed points forRweakly commuting maps in fuzzy metric spaces, Indian J. Pure Appl. Math.30 (1999), 419{423], Chugh and Kumar [Common xed point theorem in fuzzymetric spaces, Bull. Cal. Math. Soc. 94 (2002), 17{22] and Imdad and Ali [Somecommon xed point theorems in fuzzy metric spaces, Math. Commun. 11(2)(2006), 153163].
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B. D.
Pant
Government Degree College, Champawat, 262523, Uttarakhand, India.
Government Degree College, Champawat, 262523,
Iran


S.
Chauhan
R. H. Government Postgraduate College, Kashipur, 244713, (U. S. Nagar),
Uttarakhand, India.
R. H. Government Postgraduate College, Kashipur,
Iran
Triangle norm (tnorm)
Menger space
Fuzzy metric space
Occasionally weakly compatible mappings
Fixed point
Generalization of Titchmarsh's Theorem for the Dunkl transform
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2
Using a generalized spherical mean operator, we obtain the generalizationof Titchmarsh's theorem for the Dunkl transform for functions satisfyingthe Lipschitz condition in L2(Rd;wk), where wk is a weight function invariantunder the action of an associated reection groups.
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30


M.
El Hamma
Department of Mathematics, Faculty of Science Ain Chock, University Hassan
II, Casablanca, Morocco
Department of Mathematics, Faculty of Science
Iran


R.
Daher
Department of Mathematics, Faculty of Science Ain Chock, University Hassan
II, Casablanca, Morocco
Department of Mathematics, Faculty of Science
Iran


A.
El Houasni
Department of Mathematics, Faculty of Science Ain Chock, University Hassan
II, Casablanca, Morocco
Department of Mathematics, Faculty of Science
Iran


A.
Khadari
Department of Mathematics, Faculty of Science Ain Chock, University Hassan
II, Casablanca, Morocco
Department of Mathematics, Faculty of Science
Iran
Dunkl operator
Dunkl transform
generalized spherical mean operator
New iterative methods with seventhorder convergence for solving nonlinear equations
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2
In this paper, seventhorder iterative methods for the solution ofnonlinear equations are presented. The new iterative methods are developed byusing weight function method and using an approximation for the last derivative,which reduces the required number of functional evaluations per step. Severalexamples are given to illustrate the eciency and the performance of the newiterative methods.
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37


M.
Fardi
Department of Mathematics, Islamic Azad University, Najafabad Branch, Na
jafabad, Iran.
Department of Mathematics, Islamic Azad University
Iran


M.
Ghasemi
Department of Applied Mathematics, Faculty of Science, Shahrekord Univer
sity, Shahrekord, P. O. Box 115, Iran.
Department of Applied Mathematics, Faculty
Iran


A.
Davari
Department of Mathematics, University of Isfahan, Isfahan, Iran.
Department of Mathematics, University of
Iran
Iterative methods
Fourth order
Seventh order
Newton
convergence
Nonlinear
Equivalence of Kfunctionals and modulus of smoothness for fourier transform
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2
In Hilbert space L2(Rn), we prove the equivalence between the modulus of smoothness and the Kfunctionals constructed by the Sobolev space corresponding to the Fourier transform. For this purpose, Using a spherical meanoperator.
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43


R.
Daher
Department of Mathematics, Faculty of Science An Chock, University Hassan
II, Casablanca, Morocco
Department of Mathematics, Faculty of Science
Iran


M.
El Hamma
Department of Mathematics, Faculty of Science An Chock, University Hassan
II, Casablanca, Morocco
Department of Mathematics, Faculty of Science
Iran
Fourier transform
spherical mean operator
Kfunctionals
modulus of smoothness
The convexity of the integral operator on the class of the integral operator on the class B(mu,alpha)
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2
In this paper, we study the convexity of the integral operator
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48


L.
Stanciu
Department of Mathematics, T^argul din Vale Str., No.1, 110040, Pitesti, Arges,
Rom^ania.
Department of Mathematics, T^argul din Vale
Iran


D.
Breaz
Department of Mathematics, Alba Iulia, Str. N. Iorga, 510000, No. 1113,
Rom^ania.
Department of Mathematics, Alba Iulia, Str.
Iran
Analytic functions
Integral Operator
Starlike functions
Convex func tions
Approximating fixed points for nonexpansive mappings and generalized mixed equilibrium problems in Banach spaces
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2
We introduce a new iterative scheme for nding a common elementof the solutions set of a generalized mixed equilibrium problem and the xedpoints set of an innitely countable family of nonexpansive mappings in a Banachspace setting. Strong convergence theorems of the proposed iterative scheme arealso established by the generalized projection method. Our results generalize thecorresponding results in the literature.
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58


P.
Cholamjiak
Department of Mathematics, Faculty of Science, Chiang Mai University, Chiang
Mai 50200, Thailand
Department of Mathematics, Faculty of Science,
Iran


S.
Suantai
Department of Mathematics, Faculty of Science, Chiang Mai University, Chiang
Mai 50200, Thailand
Department of Mathematics, Faculty of Science,
Iran
Generalized mixed equilibrium problem
nonexpansive mappings
Com mon xed point
strong convergence
Generalized projection
Some results on maximal open sets
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In this paper, the notion of maximal mopen set is introduced and itsproperties are investigated. Some results about existence of maximal mopen setsare given. Moreover, the relations between maximal mopen sets in an mspaceand maximal open sets in the corresponding generated topology are considered.Our results are supported by examples and counterexamples.
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66


M.
Roohi
Department of Mathematics, Faculty of Sciences, Golestan University,, P.O.Box.
155, Gorgan, Iran.
Department of Mathematics, Faculty of Sciences,
Iran


M.
Rostamian Delavar
Young Researchers Club, Sari Branch, Islamic Azad University, Sari, Iran.
Young Researchers Club, Sari Branch, Islamic
Iran


S.
Mohammadzadeh
Islamic Azad UniversityBabol Branch, Babol, Iran.
Islamic Azad UniversityBabol Branch, Babol,
Iran
Small topology
minimal structure
maximal open set
conite subset
generated topology
Solution and stability of Tribonacci functional
equation in nonArchimedean Banach spaces
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In this paper, we prove Hyers{Ulam stability of Tribonacci functional equationf(x) = f(x 1) + f(x 2) + f(x 3)in the class of functions f : R ! X where X is a real nonarchimedean Banach space.
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74


M.
Eshaghi Gordji
Department of Mathematics, Semnan University, P. O. Box 35195363, Semnan, Iran.
Department of Mathematics, Semnan University,
Iran


M.
Naderi Parizi
Payame Noor University, Rafsanjan, Iran.
Payame Noor University, Rafsanjan, Iran.
Iran


Th. M.
Rassias
Department of Mathematics, National Technical University of Athens, Greece.
Department of Mathematics, National Technical
Iran
Hyers Ulam Stability
Real NonArchimedean Banach Space
Tribonacci Functional Equation
Approximate additive and quadratic mappings in 2Banach spaces and related topics
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Won{Gil Park [Won{Gil Park, J. Math. Anal. Appl., 376 (1) (2011) 193{202] proved the Hyers{Ulam stability of the Cauchy functional equation, the Jensen functional equation and the quadraticfunctional equation in 2{Banach spaces. One can easily see that all results of this paper are incorrect.Hence the control functions in all theorems of this paper are not correct. In this paper, we correctthese results.
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81


Y. J.
Cho
Department of Mathematics Education and the RINS, Gyeongsang National University, Chinju 660701, Korea.
Department of Mathematics Education and the
Iran


C.
Park
Research Institute for Natural Sciences, Hanyang University, Seoul 133791, Korea.
Research Institute for Natural Sciences,
Iran


M.
Eshaghi Gordji
Department of Mathematics, Semnan University, P. O. Box 35195363, Semnan, Iran.
Department of Mathematics, Semnan University,
Iran
Hyers{Ulam Stability
Cauchy Functional Equation
Jensen Functional Equation
quadratic functional equation