Halpern- and Mann-Type Algorithms for Fixed Points and Inclusion Problems on Hadamard Manifolds. (26th April 2019)

• Record Type: Journal Article
• Authors: Al-Homidan, Suliman; Ansari, Qamrul Hasan; Babu, Feeroz
• Is Part Of: Numerical functional analysis and optimization. Volume 40:Number 6(2019)
• Page Start: 621
• Page End: 653
• Publication Date: 2019-04-26
• Subjects: Fixed points -- Hadamard manifolds -- Halpern-type algorithm -- inclusions problems -- Mann-type algorithm -- maximal monotone vector fields -- nonexpansive mappings -- Riemannian metric; 49J53 -- 58E35 -- 47J22 -- 58C30 -- 47J25 -- 49J40 -- 47J20 -- 47H05; Functional analysis -- Periodicals; Numerical analysis -- Periodicals; Mathematical optimization -- Periodicals; Numerical Analysis, Computer-Assisted; 515.705
• DOI: 10.1080/01630563.2018.1553887
• Languages: English
• ISSNs: 0163-0563

Abstract

Abstract: In this article, we consider an inclusion problem which is defined by means of a sum of a single-valued vector field and a set-valued vector field defined on a Hadamard manifold. We propose Halpern-type and Mann-type algorithms for finding a common point of the set of fixed points of a nonexpansive mapping and the set of solutions of the inclusion problem defined on a Hadamard manifold. Some particular cases of our problem and algorithm are also discussed. We study the convergence of the proposed algorithm to a common point of the set of fixed points of a nonexpansive mapping and the set of solutions of the inclusion problem defined on a Hadamard manifold. As applications of our results and algorithms, we derive the solution methods and their convergence results for the optimization problems, variational inequality problems and equilibrium problems in the setting of Hadamard manifolds.