Abstract and Applied Analysis

Common fixed points of one-parameter nonexpansive semigroups in strictly convex Banach spaces

Tomonari Suzuki

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Abstract

One of our main results is the following convergence theorem for one-parameter nonexpansive semigroups: let C be a bounded closed convex subset of a Hilbert space E , and let { T ( t ) : t + } be a strongly continuous semigroup of nonexpansive mappings on C . Fix u C and t 1 , t 2 + with t 1 < t 2 . Define a sequence { x n } in C by x n = ( 1 α n ) / ( t 2 t 1 ) t 1 t 2 T ( s ) x n d s + α n u for n , where { α n } is a sequence in ( 0 , 1 ) converging to 0 . Then { x n } converges strongly to a common fixed point of { T ( t ) : t + } .

Article information

Source
Abstr. Appl. Anal., Volume 2006 (2006), Article ID 58684, 10 pages.

Dates
First available in Project Euclid: 30 January 2007

Permanent link to this document
https://projecteuclid.org/euclid.aaa/1170202980

Digital Object Identifier
doi:10.1155/AAA/2006/58684

Mathematical Reviews number (MathSciNet)
MR2211674

Zentralblatt MATH identifier
1130.47036

Citation

Suzuki, Tomonari. Common fixed points of one-parameter nonexpansive semigroups in strictly convex Banach spaces. Abstr. Appl. Anal. 2006 (2006), Article ID 58684, 10 pages. doi:10.1155/AAA/2006/58684. https://projecteuclid.org/euclid.aaa/1170202980


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