The shrinking projection method for solving generalized equilibrium problems and common fixed points for asymptotically quasi-ϕ-nonexpansive mappings

• Published in: Fixed point theory and applications (Hindawi Publishing Corporation) Vol. 2011; no. 1; p. 9
• Main Authors: Saewan, Siwaporn, Kumam, Poom
• Format: Journal Article
• Language: English
• Published: Cham Springer International Publishing 23.06.2011; BioMed Central Ltd; SpringerOpen
• Subjects: Analysis; Applications of Mathematics; Asymptotically quasi-ϕ-nonexpansive mapping; Banach spaces; Differential Geometry; Generalized mixed equilibrium problem; Mathematical and Computational Biology; Mathematics; Mathematics and Statistics; S. Park's Contribution to the Development of Fixed Point Theory and KKM Theory; Strong convergence theorem; Topology; Variational inequality; nonexpansive mapping; Generalized mixed equilibrium problem; Banach spaces; Strong convergence theorem; Variational inequality; Asymptotically quasi
• ISSN: 1687-1812; 1687-1820; 1687-1812
• DOI: 10.1186/1687-1812-2011-9

In this article, we introduce a new hybrid projection iterative scheme based on the shrinking projection method for finding a common element of the set of solutions of the generalized mixed equilibrium problems and the set of common fixed points for a pair of asymptotically quasi- ϕ -nonexpansive mappings in Banach spaces and set of variational inequalities for an α -inverse strongly monotone mapping. The results obtained in this article improve and extend the recent ones announced by Matsushita and Takahashi (Fixed Point Theory Appl. 2004(1):37-47, 2004), Qin et al. (Appl. Math. Comput. 215:3874-3883, 2010), Chang et al. (Nonlinear Anal. 73:2260-2270, 2010), Kamraksa and Wangkeeree (J. Nonlinear Anal. Optim.: Theory Appl. 1(1):55-69, 2010) and many others. AMS Subject Classification : 47H05, 47H09, 47J25, 65J15.