Strong convergence theorems by hybrid projection methods for equilibrium problems and fixed point problems of the asymptotically quasi-ϕ-nonexpansive mappings

• Published in: Fixed point theory and applications (Hindawi Publishing Corporation) Vol. 2011; no. 1; pp. 1 - 15
• Main Author: Kim, Jong Kyu
• Format: Journal Article
• Language: English
• Published: Cham Springer International Publishing 24.06.2011; BioMed Central Ltd; SpringerOpen
• Subjects: Analysis; Applications of Mathematics; Asymptotic properties; Asymptotically quasi-ϕ-nonexpansive mapping; Banach space; Classification; Convergence; Differential Geometry; Equilibrium problem; Fixed points (mathematics); Generalized projection; Lower semi-continuous; Mapping; Mathematical analysis; Mathematical and Computational Biology; Mathematics; Mathematics and Statistics; Projection; Relatively non-expansive mapping; S. Park's Contribution to the Development of Fixed Point Theory and KKM Theory; Theorems; Topology; nonexpansive mapping; Relatively non-expansive mapping; Equilibrium problem; Lower semi-continuous; Generalized projection; Asymptotically quasi
• ISSN: 1687-1812; 1687-1820; 1687-1812
• DOI: 10.1186/1687-1812-2011-10

We consider a hybrid projection method for finding a common element in the fixed point set of an asymptotically quasi- ϕ -nonexpansive mapping and in the solution set of an equilibrium problem. Strong convergence theorems of common elements are established in a uniformly smooth and strictly convex Banach space which has the Kadec-Klee property. 2000 Mathematics subject classification : 47H05, 47H09, 47H10, 47J25