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

✍ Scribed by Narin Petrot; Kriengsak Wattanawitoon; Poom Kumam

• Publisher: Elsevier
• Year: 2010
• Tongue: English
• Weight: 381 KB
• Volume: 4
• Category: Article
• ISSN: 1751-570X
• DOI: 10.1016/j.nahs.2010.03.008

✦ Synopsis

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.