<abstract xmlns="http://www.w3.org/1999/xhtml"><p> In this paper, we first prove a path convergence theorem for a nonexpansive mapping in a reflexive and strictly convex Banach space which has a uniformly Gˆateaux differentiable norm and admits the duality mapping jφ, where φ is a gauge function on [0,∞). Using this result, strong convergence theorems for common fixed points of a countable family of nonexpansive mappings are established.</p></abstract>

In this paper, we first prove a path convergence theorem for a nonexpansive mapping in a reflexive and strictly convex Banach space which has a uniformly Gˆateaux differentiable norm and admits the duality mapping jφ, where φ is a gauge function on [0,∞). Using this result, strong convergence theorems for common fixed points of a countable family of nonexpansive mappings are established.

Strong convergence theorems for a sequence of nonexpansive mappings with gauge functions

School of Science, University of Phayao, Phayao 56000, Thailand

Department of Mathematics Education and the RINS, Gyeongsang National University, Jinju 660-701, Republic of Korea

Department of Mathematics, Faculty of Science, Chiang Mai University, Chiang Mai 50200, Thailand

Analele ştiinţifice ale Universităţii "Ovidius" Constanţa. Seria Matematică

In this paper, we first prove a path convergence theorem for a nonexpansive mapping in a reflexive and strictly convex Banach space which has a uniformly...

Strong convergence theorems for a sequence of nonexpansive mappings with gauge functions

Published Online: Jul 30, 2013

Page range: 183 - 200

DOI: https://doi.org/10.2478/auom-2013-0011

This content is open access.