• Nonlinear Functional Analysis and Applications
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• 제26권4호
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• pp.663-684
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• 2021

In this paper, we present some fixed point results for a general class of nonexpansive mappings in the framework of Banach space and also proposed a new iterative scheme for approximating the fixed point of this class of mappings in the frame work of uniformly convex Banach spaces. Furthermore, we establish some basic properties and convergence results for our new class of mappings in uniformly convex Banach spaces. Finally, we present an application to nonlinear integral equation and also, a numerical example to illustrate our main result and then display the efficiency of the proposed algorithm compared to different iterative algorithms in the literature with different choices of parameters and initial guesses. The results obtained in this paper improve, extend and unify some related results in the literature.

• Journal of applied mathematics & informatics
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• 제33권3_4호
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• pp.401-415
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• 2015

In this paper, we propose a modified proximal point algorithm which consists of a resolvent operator technique step followed by a generalized projection onto a moving half-space for approximating a solution of a variational inclusion involving a maximal monotone mapping and a monotone, bounded and continuous operator in Banach spaces. The weak convergence of the iterative sequence generated by the algorithm is also proved.

• East Asian mathematical journal
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• 제26권3호
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• pp.337-350
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• 2010

Strong convergence theorem of the explicit viscosity iterative scheme involving the sunny nonexpansive retraction for nonexpansive nonself-mappings is established in a reflexive and strictly convex Banach spaces having a weakly sequentially continuous duality mapping. The main result improves the corresponding result of [19] to the more general class of mappings together with certain different control conditions.

• Kyungpook Mathematical Journal
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• 제47권1호
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• pp.77-79
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• 2007

In this note we point out how a theorem of Gamelin and Garnett from function theory can be used to establish a spectral mapping theorem for an arbitrary contraction and an associated class of $H^{\infty}$-functions.

• East Asian mathematical journal
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• 제17권1호
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• pp.57-70
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• 2001

In this paper, we introduce a class of generalized quasivariational inclusions for fuzzy mappings and show its equivalence with a class of fixed point problems. Using this equivalence, we develop the Mann and Ishikawa type perturbed iterative algorithms for this class of generalized quasivariational inclusions. Further, we prove the existence of solutions for the class of generalized quasivariational inclusions and discuss the convergence criteria for the perturbed algorithms.

• 대한수학회보
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• 제30권2호
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• pp.187-191
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• 1993

In this note we prove the following result: Let A be a complex Banach *-algebra with continuous involution and let B be an $A^{*}$-algebra./T(A) = B. Then T is continuous (Theorem 2). From above theorem some others results of special interest and some well-known results follow. (Corollaries 3,4,5,6 and 7). We close this note with some generalizations and some remarks (Theorems 8.9.10 and question). Throughout this note we consider only complex algebras. Let A and B be complex algebras. A linear mapping T from A into B is called jordan homomorphism if T( $x^{1}$) = (Tx)$^{2}$ for all x in A. A linear mapping T : A .rarw. B is called spectrally-contractive mapping if .rho.(Tx).leq..rho.(x) for all x in A, where .rho.(x) denotes spectral radius of element x. Any homomorphism algebra is a spectrally-contractive mapping. If A and B are *-algebras, then a homomorphism T : A.rarw.B is called *-homomorphism if (Th)$^{*}$=Th for all self-adjoint element h in A. Recall that a Banach *-algebras is a complex Banach algebra with an involution *. An $A^{*}$-algebra A is a Banach *-algebra having anauxiliary norm vertical bar . vertical bar which satisfies $B^{*}$-condition vertical bar $x^{*}$x vertical bar = vertical bar x vertical ba $r^{2}$(x in A). A Banach *-algebra whose norm is an algebra $B^{*}$-norm is called $B^{*}$-algebra. The *-semi-simple Banach *-algebras and the semi-simple hermitian Banach *-algebras are $A^{*}$-algebras. Also, $A^{*}$-algebras include $B^{*}$-algebras ( $C^{*}$-algebras). Recall that a semi-prime algebra is an algebra without nilpotents two-sided ideals non-zero. The class of semi-prime algebras includes the class of semi-prime algebras and the class of prime algebras. For all concepts and basic facts about Banach algebras we refer to [2] and [8].].er to [2] and [8].].

• Journal of Computing Science and Engineering
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• 제2권1호
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• pp.44-73
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• 2008

There is general agreement that the problem of data semantics has to be addressed for XML data to become machine-processable. This problem can be tackled by defining a semantic mapping between an XML schema and an ontology. Unfortunately, creating such mappings is a tedious, time-consuming, and error-prone task. To alleviate this problem, we present a solution that heuristically discovers semantic mappings between XML schemas and ontologies. The solution takes as input an initial set of simple correspondences between element attributes in an XML schema and class attributes in an ontology, and then generates a set of mapping formulas. Once such a mapping is created, it is important and necessary to maintain the consistency of the mapping when the associated XML schema and ontology evolve. In this paper, we first offer a mapping formalism to represent semantic mappings. Second, we present our heuristic mapping discovery algorithm. Third, we show through an empirical study that considerable effort can be saved when discovering complex mappings by using our prototype tool. Finally, we propose a mapping maintenance plan dealing with schema evolution. Our study provides a set of effective solutions for building sustainable semantic integration systems for XML data.

• 대한수학회보
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• 제52권5호
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• pp.1607-1619
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• 2015

We investigate some generalization of a class of Hankel-Clifford transformations having Fox H-function as part of its kernel on a class of Boehmians. The generalized transform is a one-to-one and onto mapping compatible with the classical transform. The inverse Hankel-Clifford transforms are also considered in the sense of Boehmians.

• Journal of applied mathematics & informatics
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• 제5권2호
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• pp.357-372
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• 1998

In this paper we introduce and study a new class of random completely generalized strongly nonlinear quasi -comple- mentarity problems with non-compact valued random fuzzy map-pings and construct some new iterative algorithms for this kind of random fuzzy quasi-complementarity problems. We also prove the existence of random solutions for this class of random fuzzy quasi-complementarity problems and the convergence of random iterative sequences generated by the algorithms.

• 한국지능시스템학회논문지
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• 제5권1호
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• pp.3-14
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• 1995

In this paper we introduce the class of fuzzy almost contrinuous mappings. It contains the class of fuzzy continuous mappings and is contained in the class of fuzzy weakly continuous mappings. In section 3 we discuss various properties of such mappings. In section 4 we also introduce the notion of fuzzy almost quasi-compact mappings and give relations between fuzzy almost quasi-compact mappings and the mapping which are introduced in section 2 and 3.