Strong convergence theorems of the Halpern-Mann’s mixed iteration for a totally quasi-ϕ-asymptotically nonexpansive nonself multi-valued mapping in Banach spaces

Strong convergence theorems of the Halpern-Mann’s mixed iteration for a totally quasi-φ-asymptotically nonexpansive nonself multi-valued mapping in Banach spaces

In this paper, we introduce a class of totally quasi-φ-asymptotically nonexpansive nonself multi-valued mapping to modify the Halpern-Mann-type iteration algorithm for a totally quasi-φ-asymptotically nonexpansive nonself multi-valued mapping, which has the strong convergence under a limit condition only in the framework of Banach spaces. Our results are applied to study the approximation probl...

Strong Convergence Theorems of Nonself Nonexpansive Mapping in Banach Spaces

In this paper, we obtain the strong convergence of a Halpern type iterative scheme to a fixed point of nonself nonexpansive mapping in Banach spaces. Our results improve and extend the corresponding results of Jung [6], Song [12,13], Aoyama [2]. Mathematics Subject Classification: 47H09, 47J25

Strong convergence theorems for equilibrium problems and quasi-φ-asymptotically nonexpansive mappings in Banach spaces

In this paper, we introduce two modified Mann-type iterative algorithms for finding a common element of the set of common fixed points of a family of quasi-φ-asymptotically nonexpansive mappings and the set of solutions of an equilibrium problem in Banach spaces. Then we study the strong convergence of the algorithms. Our results improve and extend the corresponding results announced by many ot...

Strong Convergence Theorems for Modifying Halpern Iterations for Quasi-Asymptotically Nonexpansive Multivalued Mapping in Banach Spaces with Applications

Throughout this paper, we denote byN and R the sets of positive integers and real numbers, respectively. Let D be a nonempty closed subset of a real Banach space X. A mapping T : D → D is said to be nonexpansive, if ‖Tx − Ty‖ ≤ ‖x − y‖, for all x, y ∈ D. Let N D and CB D denote the family of nonempty subsets and nonempty closed bounded subsets of D, respectively. The Hausdorff metric on CB D is...

Total quasi-φ-asymptotically nonexpansive semigroups and strong convergence theorems in Banach spaces