A modified Halpern-type iterative method of a system of equilibrium problems and a fixed point for a totally quasi-\(\phi\)-asymptotically nonexpansive mapping in a Banach space
Summary: 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-\(\phi\)-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 \textit{S. S. Chang} et al. [Appl. Math. Comput. 218, No.~11, 6489--6497 (2012; Zbl 1252.65097)] and some others.
totally quasi-\(\phi\)-asymptotically nonexpansive mapping
scientific article; zbMATH DE number 6106304
scientific article