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10 articles for “Banach Spaces”
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Research ArticleOpen accessPhrase in the titleConvergence Results for Fixed Point Problems of Accretive Operators in Banach SpacesChioma Lydia Ejikeme, Mujahid Abbas, Dennis Ferdinand AgbebakuThis paper deals with the approximate solutions of accretive maps in a uniformly convex Banach space. A weak convergence of a three - step iterative scheme involving the resolvents of accretive operators is proved. The main result is applied to a convex minimization problem in Hilbert spaces. In particular, the minimizer of a convex and proper lower semi-continuous function defined … …Journal of Mathematics and Statistics, Vol. 16, Issue 1 · 31 Jul 2020 · 6,467 accessesView PDFCite
Research ArticleOpen accessPhrase in the titleStrong Convergence Theorems for Fixed Points of Asymptotically Nonexpansive Mappings in Uniformly Smooth Banach SpacesOlusegun Olawale OwojoriIn this work, we establish strong convergence of the improved modified three-step iteration methods for asymptotically nonexpansive operators in uniformly smooth and convex Banach spaces. Our results generalize the previous results of Schu [10], Osilike and Aniagbosor [5], Xu and Noor [13], as well as Owojori and Imoru [7] among others. …Journal of Mathematics and Statistics, Vol. 1, Issue 2 · 30 Jun 2005 · 5,996 accessesView PDFCite
Research ArticleOpen accessPhrase in the titleApproximation Methods for Fixed Points of Quasi-contractive Mappings in Arbitrary Real Banach SpacesOlusegun O. OwojoriOwojori and Imoru [1] introduced some iteration methods and investigated its convergence for pseudocontractive and accretive operators in arbitrary Banach spaces. In this work, strong convergence results are established for fixed points of a general type of quasicontractive mappings in arbitrary real Banach spaces. Our results here represent some improvements on the earlier results of Owojori and Imoru [1], Naimpally … …Journal of Mathematics and Statistics, Vol. 1, Issue 2 · 30 Jun 2005 · 6,159 accessesView PDFCite
Research ArticleOpen accessIn the keywordsGeneralization of Banach Contraction Principle in Two DirectionsE. El-Shobaky, Sahar Mohamed Ali, Montaser Saudi AliWe showed that the generalized contraction mapping defined on a closed convex subset of a weakly Cauchy normed space has a unique fixed point. Moreover, the sequence of iterates of any element in the domain of the given mapping is converging strongly to the fixed point of such a mapping. …Journal of Mathematics and Statistics, Vol. 3, Issue 3 · 30 Sep 2007 · 6,763 accessesView PDFCite
Research ArticleOpen accessIn the keywordsReduced Assumption in the Banach Contraction PrincipleSahar M. AliIn this study we introduce a novel class of normed spaces called weakly Cauchy normed spaces not necessarily complete in general and proved the existence of a fixed point of contraction mappings in these spaces, this is weaker assumption than the completeness assumption imposed on the given normed space on the other side the contraction condition valid only on a … …Journal of Mathematics and Statistics, Vol. 2, Issue 1 · 31 Mar 2006 · 6,828 accessesView PDFCite
Research ArticleOpen accessIn the abstractMeasurable Functional Calculi and Spectral TheoryMykola YaremenkoIn this article, the spectral theory is considered, we study the spectral families and their correspondence to the operators on the reflexive Banach spaces; assume A is a well-bounded operator on reflexive Lebesgue spaces then the operator A is a scalar type spectral operator. The main goals are to obtain the characterization of the well-bounded operators in the terms of … …Journal of Mathematics and Statistics, Vol. 18, Issue 1 · 6 Jul 2022 · 6,422 accessesView PDFCite
Research ArticleOpen accessIn the abstractThe Banach space mp(X), for 1 ≤ pNaim L. BrahaProblem statement: In the theory of Banach spaces one of the problems which describes geometric property of Banach spaces is Banach-Saks Property. In this context we were known many Banach spaces which had this property such as Lp[0, 1] for 1 < p ≤ 2. Approach: Following the sequential structure of the Banach sequence space mp(X), for 1 ≤ p … …Journal of Mathematics and Statistics, Vol. 5, Issue 1 · 31 Mar 2009 · 7,772 accessesView PDFCite
Research ArticleOpen accessIn the abstractFixed Points of Non-expansive Operators on Weakly Cauchy Normed SpacesSahar Mohamed AliWe proved the existence of fixed points of non-expansive operators defined on weakly Cauchy spaces in which parallelogram law holds, the given normed space is not necessarily be uniformly convex Banach space or Hilbert space, we reduced the completeness and the uniform convexity assumptions which imposed on the given normed space. …Journal of Mathematics and Statistics, Vol. 3, Issue 2 · 30 Jun 2007 · 6,548 accessesView PDFCite
Research ArticleOpen accessAll words, across the recordFixed Point Theorems for Mappings Satisfying Weak Nonexpansivity Condition (Weak Contractivity Condition) into (from) Cartesian Products Normed SpacesSahar Mohamed Ali Abou BakrThis paper suggests new types of weak nonexpansive mappings defined from normed space X into its Cartesian product X × X, studies the main features of the fixed points for those mappings and extends the concept of (C)-contractivity condition introduced in some previous research papers. On other side, it introduces new types of contraction mappings with a mixed monotone property; … …Journal of Mathematics and Statistics, Vol. 13, Issue 2 · 11 Apr 2017 · 6,966 accessesView PDFCite
Research ArticleOpen accessAll words, across the recordGENERAL CONTRACTIVE MAPPING CONDITION OF FUZZY METRIC SPACES IN FIXED POINT THEOREMRamasamy Mohan Raj, Veerachamy Malliga DeviIn several ways, related fixed point theorems on two or three metric spaces have been demonstrated. By applying contractive condition of integral type for class of weakly compatible maps in uncompleted intuitionistic fuzzy metric spaces without considering any continuous mappings, in this paper, we verify some frequent fixed point theorems for different mappings. …Journal of Mathematics and Statistics, Vol. 10, Issue 1 · 6 Feb 2014 · 6,850 accessesView PDFCite