Journal
NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS
Volume 72, Issue 6, Pages 2896-2908Publisher
PERGAMON-ELSEVIER SCIENCE LTD
DOI: 10.1016/j.na.2009.11.034
Keywords
Relatively nonexpansive mappings; Generalized projection; Equilibrium problem; Common fixed points
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Funding
- The Thailand Research Fund
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In this paper, we prove a strong convergence theorem by the hybrid method for a countable family of relatively nonexpansive mappings in a Banach space. We also establish a new control condition for the sequence of mappings {T-n} which is weaker than the control condition in Lemma 3.1 of Aoyama et al. [K. Aoyama, Y. Kimura, W. Takahashi and M. Toyoda, Approximation of common fixed points of a countable family of nonexpansive mappings in a Banach space, Nonlinear Anal. 67 (2007) 2350-2360]. Moreover, we apply our results for finding a common fixed point of two relatively nonexpansive mappings in a Banach space and an element of the set of solutions of an equilibrium problem in a Banach space, respectively. Our results are applicable to a wide class of mappings. (C) 2009 Elsevier Ltd. All rights reserved.
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