2012
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2
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81
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On the maximal ideal space of extended polynomial and rational uniform algebras
https://ijnaa.semnan.ac.ir/article_32.html
10.22075/ijnaa.2012.32
1
Let $K$ and $X$ be compact plane sets such that $Ksubseteq X$. Let $P(K)$ be the uniform closure of polynomials on $K$. Let $R(K)$ be the closure of rational functions K with poles off $K$. Define $P(X,K)$ and $R(X,K)$ to be the uniform algebras 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 $C(X)$ such that $f_K = 0$. In this paper, we show that every nonzero complex homomorphism' on $CZ(X,K)$ is an evaluation homomorphism $e_z$ for some $z$ in $Xsetminus K$. By considering this fact, we characterize the maximal ideal space of the uniform algebra $P(X,K)$. Moreover, we show that the uniform algebra $R(X,K)$ is natural.
0

1
12


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


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


D.
Alimohammadi
Department of Mathematics, Faculty of Science, Arak University, Arak, 38156
88349, Iran.
Iran
Maximal ideal space
uniform algebras
nonzero complex homomorphism
1

Common fixed point theorems for occasionally weakly compatible mappings in Menger spaces and applications
https://ijnaa.semnan.ac.ir/article_34.html
10.22075/ijnaa.2012.34
1
In 2008, AlThagafi 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 owc maps) which is more general than all the commutativity concepts. In the present paper, we prove common fixed point theorems for families of owc maps in Menger spaces. As applications to our results, we obtain the corresponding fixed point theorems in fuzzy metric spaces. Our results improve and extend the results of Kohli and Vashistha [Common fixed point theorems in probabilistic metric spaces, Acta Math. Hungar. 115(12) (2007), 3747], Vasuki [Common fixed points for Rweakly commuting maps in fuzzy metric spaces, Indian J. Pure Appl. Math. 30 (1999), 419{423], Chugh and Kumar [Common fixed point theorem in fuzzy metric spaces, Bull. Cal. Math. Soc. 94 (2002), 17{22] and Imdad and Ali [Some common fixed point theorems in fuzzy metric spaces, Math. Commun. 11(2) (2006), 153163].
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13
23


B. D.
Pant
Government Degree College, Champawat, 262523, Uttarakhand, India
India


S.
Chauhan
R. H. Government Postgraduate College, Kashipur, 244713, (U. S. Nagar), Uttarakhand, India
India
Triangle norm (tnorm)
Menger space
Fuzzy metric space
Occasionally weakly compatible mappings
Fixed point
1

Generalization of Titchmarsh's Theorem for the Dunkl transform
https://ijnaa.semnan.ac.ir/article_36.html
10.22075/ijnaa.2012.36
1
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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24
30


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


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


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


A.
Khadari
Department of Mathematics, Faculty of Science Ain Chock, University Hassan
II, Casablanca, Morocco
Iran
Dunkl operator
Dunkl transform
generalized spherical mean operator
1

New iterative methods with seventhorder convergence for solving nonlinear equations
https://ijnaa.semnan.ac.ir/article_39.html
10.22075/ijnaa.2012.39
1
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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31
37


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


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


A.
Davari
Department of Mathematics, University of Isfahan, Isfahan, Iran.
Iran
Iterative methods
Fourth order
Seventh order
Newton
convergence
Nonlinear
1

Equivalence of $K$functionals and modulus of smoothness for Fourier transform
https://ijnaa.semnan.ac.ir/article_40.html
10.22075/ijnaa.2012.40
1
In Hilbert space $L^2(mathbb{R}^n)$, we prove the equivalence between the modulus of smoothness and the $K$functionals constructed by the Sobolev space corresponding to the Fourier transform. For this purpose, using a spherical mean operator.
0

38
43


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


M.
El Hamma
Department of Mathematics, Faculty of Science Ain Chock, University Hassan II, Casablanca, Morocco
Morocco
Fourier Transform
spherical mean operator
Kfunctionals
modulus of smoothness
1

The convexity of the integral operator on the class of $B(mu,alpha)$
https://ijnaa.semnan.ac.ir/article_41.html
10.22075/ijnaa.2012.41
1
In this paper, we study the convexity of the integral operator $int_0^zprod_{i=1}^n(te^{f_i(t)})^{gamma_i}dt$ where the function $f_i, iin{1,2,ldots,n}$ satisfy the condition
$$f_i'(z)(frac{z}{f_i(z)})^{mu_i}1<1alpha_i,quad iin{1,2,ldots,n}.$$
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44
48


L.
Stanciu
Department of Mathematics, Targul din Vale Str., No.1, 110040, Pitesti, Arges, Romania
Romania


D.
Breaz
Department of Mathematics, Alba Iulia, Str. N. Iorga, 510000, No. 1113,
Romania
Romania
Analytic functions
Integral Operator
Starlike functions
Convex functions
1

Approximating fixed points for nonexpansive mappings and generalized mixed equilibrium problems in Banach spaces
https://ijnaa.semnan.ac.ir/article_43.html
10.22075/ijnaa.2012.43
1
We introduce a new iterative scheme for finding a common element of the solutions set of a generalized mixed equilibrium problem and the fixed points set of an infinitely countable family of nonexpansive mappings in a Banach space setting. Strong convergence theorems of the proposed iterative scheme are also established by the generalized projection method. Our results generalize the corresponding results in the literature.
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49
58


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


S.
Suantai
Department of Mathematics, Faculty of Science, Chiang Mai University, Chiang
Mai 50200, Thailand
Thailand
Generalized mixed equilibrium problem
nonexpansive mappings
Common fixed point
strong convergence
Generalized projection
1

Some results on maximal open sets
https://ijnaa.semnan.ac.ir/article_44.html
10.22075/ijnaa.2012.44
1
In this paper, the notion of maximal mopen set is introduced and its properties are investigated. Some results about existence of maximal mopen sets are given. Moreover, the relations between maximal mopen sets in an mspace and maximal open sets in the corresponding generated topology are considered. Our results are supported by examples and counterexamples.
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59
66


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


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


S.
Mohammadzadeh
Islamic Azad UniversityBabol Branch, Babol, Iran.
Iran
Small topology
minimal structure
maximal open set
conite subset
generated topology
1

Solution and stability of Tribonacci functional equation in nonArchimedean Banach spaces
https://ijnaa.semnan.ac.ir/article_54.html
10.22075/ijnaa.2012.54
1
In this paper, we prove Hyers{Ulam stability of Tribonacci functional equation$$f(x) = f(x  1) + f(x  2) + f(x  3)$$in the class of functions $f : mathbb{R} to X$ where $X$ is a real nonArchimedean Banach space.
0

67
74


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


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


Th. M.
Rassias
Department of Mathematics, National Technical University of Athens, Greece
Greece
Hyers Ulam Stability
Real NonArchimedean Banach Space
Tribonacci Functional Equation
1

Approximate additive and quadratic mappings in 2Banach spaces and related topics
https://ijnaa.semnan.ac.ir/article_55.html
10.22075/ijnaa.2012.55
1
WonGil Park [WonGil Park, J. Math. Anal. Appl., 376 (1) (2011) 193{202] proved the HyersUlam stability of the Cauchy functional equation, the Jensen functional equation and the quadratic functional equation in 2Banach 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 correct these results.
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75
81


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


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


M.
Eshaghi Gordji
Department of Mathematics, Semnan University, P. O. Box 35195363, Semnan, Iran.
Iran
HyersUlam stability
Cauchy Functional Equation
Jensen Functional Equation
quadratic functional equation