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August 2017 On the weak convergence theorem for nonexpansive semigroups in Banach spaces
Rongjie Yao, Liping Yang
Ann. Funct. Anal. 8(3): 341-349 (August 2017). DOI: 10.1215/20088752-0000018X

Abstract

Assume that K is a closed convex subset of a uniformly convex Banach space E, and assume that {T(s)}s>0 is a nonexpansive semigroup on K. By using the following implicit iteration sequence {xn} defined by xn=(1αn)xn1+αn1tn0tnT(s)xnds,n1, the main purpose of this paper is to establish a weak convergence theorem for the nonexpansive semigroup {T(s)}s>0 in uniformly convex Banach spaces without the Opial property. Our results are different from some recently announced results.

Citation

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Rongjie Yao. Liping Yang. "On the weak convergence theorem for nonexpansive semigroups in Banach spaces." Ann. Funct. Anal. 8 (3) 341 - 349, August 2017. https://doi.org/10.1215/20088752-0000018X

Information

Received: 27 May 2016; Accepted: 26 October 2016; Published: August 2017
First available in Project Euclid: 22 April 2017

zbMATH: 06754361
MathSciNet: MR3689997
Digital Object Identifier: 10.1215/20088752-0000018X

Subjects:
Primary: 47H09
Secondary: 47H10

Rights: Copyright © 2017 Tusi Mathematical Research Group

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Vol.8 • No. 3 • August 2017
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