Strong convergence of Krasnoselskii and Mann's type sequences for one-parameter nonexpansive semigroups without Bochner integrals |
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Authors: | Tomonari Suzuki |
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Institution: | Department of Mathematics, Kyushu Institute of Technology, 1-1, Sensuicho, Tobataku, Kitakyushu 804-8550, Japan |
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Abstract: | In this paper, we prove Krasnoselskii and Mann's type convergence theorems for nonexpansive semigroups without using Bochner integral and without assuming the strict convexity of Banach spaces. One of our main results is the following: let C be a compact convex subset of a Banach space E and let be a one-parameter strongly continuous semigroup of nonexpansive mappings on C. Let {tn} be a sequence in 0,∞) satisfying |
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Keywords: | One-parameter nonexpansive semigroup Common fixed point Convergence theorem |
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