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

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  • Kyung Soo Kim

Abstract

The purpose of this paper is to study modified Halpern type and Ishikawa type iteration for a semigroup of relatively nonexpansive mappings on a nonempty closed convex subset of a Banach space with respect to a sequence of asymptotically left invariant means defined on an appropriate invariant subspace of , where 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 , where .

Suggested Citation

  • Kyung Soo Kim, 2014. "Invariant Means and Reversible Semigroup of Relatively Nonexpansive Mappings in Banach Spaces," Abstract and Applied Analysis, Hindawi, vol. 2014, pages 1-9, July.
    • Handle: RePEc:hin:jnlaaa:694783
    DOI: 10.1155/2014/694783
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