Annals of Functional Analysis

On the weak convergence theorem for nonexpansive semigroups in Banach spaces

Rongjie Yao and Liping Yang

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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.

Article information

Ann. Funct. Anal., Volume 8, Number 3 (2017), 341-349.

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

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 47H09: Contraction-type mappings, nonexpansive mappings, A-proper mappings, etc.
Secondary: 47H10: Fixed-point theorems [See also 37C25, 54H25, 55M20, 58C30]

nonexpansive semigroups fixed point implicit iteration scheme uniformly convex Banach spaces


Yao, Rongjie; Yang, Liping. On the weak convergence theorem for nonexpansive semigroups in Banach spaces. Ann. Funct. Anal. 8 (2017), no. 3, 341--349. doi:10.1215/20088752-0000018X.

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