An Ishikawa Iteration Scheme for two Nonlinear Mappings in CAT(0) Spaces

Kritsana Sokhuma

doi:10.5666/KMJ.2019.59.4.665

Article

KYUNGPOOK Math. J. 2019; 59(4): 665-678

Published online December 23, 2019

An Ishikawa Iteration Scheme for two Nonlinear Mappings in CAT(0) Spaces

Kritsana Sokhuma

Department of Mathematics, Faculty of Science and Technology, Phranakhon Rajabhat University, Bangkok 10220, Thailand
e-mail : k_sokhuma@yahoo.co.th

Received: December 9, 2017; Revised: December 10, 2018; Accepted: December 11, 2018

Abstract

Go to

Abstract

We construct an iteration scheme involving a hybrid pair of mappings, one a single-valued asymptotically nonexpansive mapping t and the other a multivalued nonexpansive mapping T, in a complete CAT(0) space. In the process, we remove a restricted condition (called the end-point condition) from results of Akkasriworn and Sokhuma [1] and and use this to prove some convergence theorems. The results concur with analogues for Banach spaces from Uddin et al. [16].

Keywords: Ishikawa iteration, CAT(0) spaces, multivalued mapping, asymptotically nonexpansive mapping.