A Modified Halpern‐TypeIterative Method of a System of Equilibrium Problems and a Fixed Point for a Totally Quasi‐ϕ‐Asymptotically Nonexpansive Mapping in a Banach Space
Preedaporn Kanjanasamranwong, Poom Kumam, Siwaporn Saewan · Journal of Applied Mathematics · 2012
The purpose of this paper is to introduce the modified Halpern‐type iterative method by the generalized f‐projection operator for finding a common solution of fixed‐point problem of a totally quasi‐ϕ‐asymptotically nonexpansive mapping and a system of equilibrium problems in a uniform smooth and strictly convex Banach space with the Kadec‐Klee property. Consequently, we prove the strong convergence for a common solution of above two sets. Our result presented in this paper generalize and improve the result of Chang et al., (2012), and some others.