International Journal Of Nonlinear Analysis And Applications
Volume:3 Issue: 2, Winter - Spring 2012

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 rational functions K with poles o K. De ne 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 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 con- sidering 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.

In 2008, Al-Thaga 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 xed point theorems for families of owc maps in Menger spaces. As applications to our results, we obtain the corresponding xed point theorems in fuzzy metric spaces. Our results improve and extend the results of Kohli and Vashistha [Common xed point theorems in probabilistic metric spaces, Acta Math. Hungar. 115(1-2) (2007), 37-47], Vasuki [Common xed points for R-weakly commuting maps in fuzzy metric spaces, Indian J. Pure Appl. Math. 30 (1999), 419{423], Chugh and Kumar [Common xed point theorem in fuzzy metric spaces, Bull. Cal. Math. Soc. 94 (2002), 17{22] and Imdad and Ali [Some common xed point theorems in fuzzy metric spaces, Math. Commun. 11(2) (2006), 153-163].

Using a generalized spherical mean operator, we obtain the generalization of Titchmarsh''s theorem for the Dunkl transform for functions satisfying the Lipschitz condition in L2(Rd;wk), where wk is a weight function invariant under the action of an associated re ection groups.

In this paper, seventh-order iterative methods for the solution of nonlinear equations are presented. The new iterative methods are developed by using weight function method and using an approximation for the last derivative, which reduces the required number of functional evaluations per step. Several examples are given to illustrate the efficiency and the performance of the new iterative methods.

In Hilbert space $mathrm{L}^{2}(mathbb{R}^{n})$, 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.

In this paper, we study the convexity of the integral operator R z0Qni=1􀀀tefi(t)
i dtwhere the functions fi, i 2 f1; 2;: ::; ng satisfy the condition f0i (z) z fi(z) i􀀀 1 < 1 􀀀 i; i 2 f1; 2;: ::; ng.

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.

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.