Abstract and Applied Analysis

Invariant Means and Reversible Semigroup of Relatively Nonexpansive Mappings in Banach Spaces

Kyung Soo Kim

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Abstract

The purpose of this paper is to study modified Halpern type and Ishikawa type iteration for a semigroup of relatively nonexpansive mappings I = { T ( s ) : s S } on a nonempty closed convex subset C of a Banach space with respect to a sequence of asymptotically left invariant means { μ n } defined on an appropriate invariant subspace of l ( S ) , where S is a semigroup. We prove that, given some mild conditions, we can generate iterative sequences which converge strongly to a common element of the set of fixed points F ( I ) , where F ( I ) = { F ( T ( s ) ) : s S } .

Article information

Source
Abstr. Appl. Anal., Volume 2014, Special Issue (2014), Article ID 694783, 9 pages.

Dates
First available in Project Euclid: 27 February 2015

Permanent link to this document
https://projecteuclid.org/euclid.aaa/1425048210

Digital Object Identifier
doi:10.1155/2014/694783

Mathematical Reviews number (MathSciNet)
MR3246353

Zentralblatt MATH identifier
07022895

Citation

Kim, Kyung Soo. Invariant Means and Reversible Semigroup of Relatively Nonexpansive Mappings in Banach Spaces. Abstr. Appl. Anal. 2014, Special Issue (2014), Article ID 694783, 9 pages. doi:10.1155/2014/694783. https://projecteuclid.org/euclid.aaa/1425048210


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