ORIGINAL_ARTICLE
On the maximal ideal space of extended polynomial and rational uniform algebras
Let $K$ and $X$ be compact plane sets such that $K\subseteq X$. 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 $X\setminus K$. 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.
https://ijnaa.semnan.ac.ir/article_32_ded7ad00ddc06fb990aa09ff3ab151bd.pdf
2012-06-01
1
12
10.22075/ijnaa.2012.32
Maximal ideal space
uniform algebras
nonzero complex homomorphism
S.
Moradi
1
Department of Mathematics, Faculty of Science, Arak University, Arak, 38156- 8-8349, Iran.
LEAD_AUTHOR
T. G.
Honary
2
Faculty of Mathematical Sciences and Computer Engineering, Teacher Train- ing University, 599 Taleghani Avenue, Tehran, 15618, I.R. Iran.
AUTHOR
D.
Alimohammadi
3
Department of Mathematics, Faculty of Science, Arak University, Arak, 38156- 8-8349, Iran.
AUTHOR
ORIGINAL_ARTICLE
Common fixed point theorems for occasionally weakly compatible mappings in Menger spaces and applications
In 2008, Al-Thagafi and Shahzad [Generalized I-nonexpansive self-maps 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(1-2) (2007), 37-47], Vasuki [Common fixed points for R-weakly 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), 153-163].
https://ijnaa.semnan.ac.ir/article_34_016d0cc127099f39b280fa0de564b210.pdf
2012-06-01
13
23
10.22075/ijnaa.2012.34
Triangle norm (t-norm)
Menger space
Fuzzy metric space
Occasionally weakly compatible mappings
Fixed point
B. D.
Pant
1
Government Degree College, Champawat, 262523, Uttarakhand, India
AUTHOR
S.
Chauhan
2
R. H. Government Postgraduate College, Kashipur, 244713, (U. S. Nagar), Uttarakhand, India
LEAD_AUTHOR
ORIGINAL_ARTICLE
Generalization of Titchmarsh's Theorem for the Dunkl transform
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.
https://ijnaa.semnan.ac.ir/article_36_9427900803b7cbbfe2f444c6f482eabb.pdf
2012-06-01
24
30
10.22075/ijnaa.2012.36
Dunkl operator
Dunkl transform
generalized spherical mean operator
M.
El Hamma
1
Department of Mathematics, Faculty of Science Ain Chock, University Hassan II, Casablanca, Morocco
LEAD_AUTHOR
R.
Daher
2
Department of Mathematics, Faculty of Science Ain Chock, University Hassan II, Casablanca, Morocco
AUTHOR
A.
El Houasni
3
Department of Mathematics, Faculty of Science Ain Chock, University Hassan II, Casablanca, Morocco
AUTHOR
A.
Khadari
4
Department of Mathematics, Faculty of Science Ain Chock, University Hassan II, Casablanca, Morocco
AUTHOR
ORIGINAL_ARTICLE
New iterative methods with seventh-order convergence for solving nonlinear equations
In this paper, seventh-order 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.
https://ijnaa.semnan.ac.ir/article_39_2cfe2327e8cdbf5111d44e9fdaca81e4.pdf
2012-06-01
31
37
10.22075/ijnaa.2012.39
Iterative methods
Fourth order
Seventh order
Newton
convergence
Nonlinear
M.
Fardi
1
Department of Mathematics, Islamic Azad University, Najafabad Branch, Na- jafabad, Iran.
LEAD_AUTHOR
M.
Ghasemi
2
Department of Applied Mathematics, Faculty of Science, Shahrekord Univer- sity, Shahrekord, P. O. Box 115, Iran.
AUTHOR
A.
Davari
3
Department of Mathematics, University of Isfahan, Isfahan, Iran.
AUTHOR
ORIGINAL_ARTICLE
Equivalence of $K$-functionals and modulus of smoothness for Fourier transform
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.
https://ijnaa.semnan.ac.ir/article_40_c81d23487ce3f62b66f897bddd94f41d.pdf
2012-06-01
38
43
10.22075/ijnaa.2012.40
Fourier Transform
spherical mean operator
K-functionals
modulus of smoothness
R.
Daher
1
Department of Mathematics, Faculty of Science Ain Chock, University Hassan II, Casablanca, Morocco
AUTHOR
M.
El Hamma
2
Department of Mathematics, Faculty of Science Ain Chock, University Hassan II, Casablanca, Morocco
LEAD_AUTHOR
ORIGINAL_ARTICLE
The convexity of the integral operator on the class of $B(\mu,\alpha)$
In this paper, we study the convexity of the integral operator $\int_0^z\prod_{i=1}^n(te^{f_i(t)})^{\gamma_i}dt$ where the function $f_i, i\in\{1,2,\ldots,n\}$ satisfy the condition
$$|f_i'(z)(\frac{z}{f_i(z)})^{\mu_i}-1|<1-\alpha_i,\quad i\in\{1,2,\ldots,n\}.$$
https://ijnaa.semnan.ac.ir/article_41_84f077cf108eac44a9ad2244e5db809c.pdf
2012-06-01
44
48
10.22075/ijnaa.2012.41
Analytic functions
Integral Operator
Starlike functions
Convex functions
L.
Stanciu
1
Department of Mathematics, Targul din Vale Str., No.1, 110040, Pitesti, Arges, Romania
LEAD_AUTHOR
D.
Breaz
2
Department of Mathematics, Alba Iulia, Str. N. Iorga, 510000, No. 11-13, Romania
AUTHOR
ORIGINAL_ARTICLE
Approximating fixed points for nonexpansive mappings and generalized mixed equilibrium problems in Banach spaces
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.
https://ijnaa.semnan.ac.ir/article_43_46906f1a1341c289e94eeac745208e92.pdf
2012-06-01
49
58
10.22075/ijnaa.2012.43
Generalized mixed equilibrium problem
nonexpansive mappings
Common fixed point
strong convergence
Generalized projection
P.
Cholamjiak
1
Department of Mathematics, Faculty of Science, Chiang Mai University, Chiang Mai 50200, Thailand
AUTHOR
S.
Suantai
2
Department of Mathematics, Faculty of Science, Chiang Mai University, Chiang Mai 50200, Thailand
LEAD_AUTHOR
ORIGINAL_ARTICLE
Some results on maximal open sets
In this paper, the notion of maximal m-open set is introduced and its properties are investigated. Some results about existence of maximal m-open sets are given. Moreover, the relations between maximal m-open sets in an m-space and maximal open sets in the corresponding generated topology are considered. Our results are supported by examples and counterexamples.
https://ijnaa.semnan.ac.ir/article_44_98b9534f8bd00671e1f9f9f07bf2b953.pdf
2012-06-01
59
66
10.22075/ijnaa.2012.44
Small topology
minimal structure
maximal open set
conite subset
generated topology
M.
Roohi
1
Department of Mathematics, Faculty of Sciences, Golestan University,, P.O.Box. 155, Gorgan, Iran.
AUTHOR
M.
Rostamian Delavar
2
Young Researchers Club, Sari Branch, Islamic Azad University, Sari, Iran.
LEAD_AUTHOR
S.
Mohammadzadeh
3
Islamic Azad University-Babol Branch, Babol, Iran.
AUTHOR
ORIGINAL_ARTICLE
Solution and stability of Tribonacci functional equation in non-Archimedean Banach spaces
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 non-Archimedean Banach space.
https://ijnaa.semnan.ac.ir/article_54_934b686783b476e9459b12a92c9ed19d.pdf
2012-06-01
67
74
10.22075/ijnaa.2012.54
Hyers Ulam Stability
Real Non-Archimedean Banach Space
Tribonacci Functional Equation
M.
Eshaghi Gordji
1
Department of Mathematics, Semnan University, P. O. Box 35195-363, Semnan, Iran.
LEAD_AUTHOR
M.
Naderi Parizi
2
Payame Noor University, Rafsanjan, Iran.
AUTHOR
Th. M.
Rassias
3
Department of Mathematics, National Technical University of Athens, Greece
AUTHOR
ORIGINAL_ARTICLE
Approximate additive and quadratic mappings in 2-Banach spaces and related topics
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 quadratic functional 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 correct these results.
https://ijnaa.semnan.ac.ir/article_55_27dbad8d0aa4f90c342927098fa87f62.pdf
2012-06-01
75
81
10.22075/ijnaa.2012.55
Hyers-Ulam stability
Cauchy Functional Equation
Jensen Functional Equation
quadratic functional equation
Y. J.
Cho
1
Department of Mathematics Education and the RINS, Gyeongsang National University, Chinju 660-701, Korea
AUTHOR
C.
Park
2
Research Institute for Natural Sciences, Hanyang University, Seoul 133-791, Korea
AUTHOR
M.
Eshaghi Gordji
3
Department of Mathematics, Semnan University, P. O. Box 35195-363, Semnan, Iran.
LEAD_AUTHOR