Hybrid Projection Algorithm for Two Finite Families of Asymptotically Quasi ϕ-Nonexpansive Mappings in Reflexive Banach Spaces

ABSTRACT

In this paper, we introduce a hybrid projection algorithm for two finite families of asymptotically quasi ϕ-nonexpansive mappings to establish a convergence theorem in smooth, strictly convex, and reflexive Banach spaces. As applications, we state the convergence of hybrid projection algorithm for two finite families of asymptotically quasi-nonexpansive mappings in Hilbert spaces and the convergence for a system of equilibrium problems.

KEYWORDS:

• Asymptotically quasi ϕ-nonexpansive mappings
• hybrid projection algorithm
• reflexive Banach space

2000 MATHEMATICS SUBJECT CLASSIFICATION:

• Primary: 47H09, 47H10
• Secondary: 47J25, 65J15

Acknowledgments

The authors sincerely thank two anonymous referees for several helpful comments. The authors also thank members of The Dong Thap Group of Mathematical Analysis and its Applications for their discussions on the manuscript.