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On the Convergence of Successive Approximations for Quasi-Nonexpansive Mappings Through Abstract Cones

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On the Convergence of Successive Approximations for Quasi-Nonexpansive Mappings Through Abstract Cones

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dc.contributor.author Williams, B. B. en
dc.contributor.author Bolen, J. C. en
dc.date.accessioned 2010-05-26T18:29:31Z en
dc.date.available 2010-05-26T18:29:31Z en
dc.date.issued 1975-07 en
dc.identifier.uri http://hdl.handle.net/10106/2182 en
dc.description.abstract In a recent paper, Petryshyn and Williamson [4] investigated the convergence of successive approximations of quasi- nonexpansive mappings in a Banach space. This paper contains an outline, in chronological order, of the main results concerning the convergence of iteration method and consequently includes a number of references. Perov and Kibenko [3] employed generalized Banach spaces to extend contraction mapping principal and to show the flexibility of such an approach in applications. See also Bernfeld and Lakshmikantham [1]. More recently, Eisenfeld and Lakshmikantham [5,6] proved some fixed point theorems in abstract cones which extend and generalize many known results. In this paper, we extend some main results of [4] to cone-valued metric spaces. In Sections 2 and 3, we give needed definitions and properties of k-metric spaces and in Section 4, we prove our main results. For convenience and for future use, we have given more details than necessary. en
dc.language.iso en_US en
dc.publisher University of Texas at Arlington en
dc.relation.ispartofseries Technical Report;29 en
dc.subject Fixed point theorems en
dc.subject K-metric spaces en
dc.subject Banach spaces en
dc.subject Contraction mapping principal en
dc.subject.lcsh Mathematics Research en
dc.title On the Convergence of Successive Approximations for Quasi-Nonexpansive Mappings Through Abstract Cones en
dc.type Technical Report en
dc.publisher.department Department of Mathematics en

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