A hybrid projection method for generalized mixed equilibrium problems and fixed point problems in Banach spaces

We introduce a hybrid projection iterative scheme for approximating a common element of the set of solutions of a generalized mixed equilibrium problem and the set of fixed points of two quasi- ϕ -nonexpansive mappings in a real uniformly convex and uniformly smooth Banach space. Then, we establish...

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Bibliographic Details
Published in:Nonlinear analysis. Hybrid systems Vol. 4; no. 4; pp. 631 - 643
Main Authors: Petrot, Narin, Wattanawitoon, Kriengsak, Kumam, Poom
Format: Journal Article
Language:English
Published: Elsevier Ltd 01.11.2010
Subjects:
Algorithms
Banach space
Convergence
Fixed points (mathematics)
Generalized mixed equilibrium problem
Hybrid projection iterative scheme
Hybrid systems
Mapping
Nonlinearity
Projection
Quasi- [formula omitted]-nonexpansive mapping
Relatively nonexpansive mapping
Strong convergence
Theorems
Strong convergence
Hybrid projection iterative scheme
Generalized mixed equilibrium problem
Quasi- ϕ -nonexpansive mapping
Relatively nonexpansive mapping
ISSN:1751-570X
Online Access:Get full text
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Summary:We introduce a hybrid projection iterative scheme for approximating a common element of the set of solutions of a generalized mixed equilibrium problem and the set of fixed points of two quasi- ϕ -nonexpansive mappings in a real uniformly convex and uniformly smooth Banach space. Then, we establish strong convergence theorems for this algorithm which are connected with results by Takahashi and Zembayashi [W. Takahashi, K. Zembayashi, Strong and weak convergence theorems for equilibrium problems and relatively nonexpansive mappings in Banach spaces, Nonlinear Analysis 70 (2009) 45–57], Qin et al. [X. Qin, Y.J. Cho, S.M. Kang, Convergence theorems of common elements for equilibrium problems and fixed point problems in Banach spaces, Journal of Computational and Applied Mathematics 225 (2009) 20–30], Wattanawitoon and Kumam [K. Wattanawitoon, P. Kumam, Strong convergence theorems by a new hybrid projection algorithm for fixed point problems and equilibrium problems of two relatively quasi-nonexpansive mappings, Nonlinear Analysis: Hybrid Systems 3 (2009) 11–20], and many others.
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ISSN:1751-570X
DOI:10.1016/j.nahs.2010.03.008