The implicit midpoint rule for nonexpansive mappings in 2-uniformly convex hyperbolic spaces. Issue 1 (22nd February 2019)

• Record Type: Journal Article
• Authors: Fukhar-ud-din, H.; Khan, A.R.
• Is Part Of: Arab journal of mathematical sciences. Volume 26:Issue 1/2(2020)
• Page Start: 95
• Page End: 105
• Publication Date: 2019-02-22
• Subjects: Uniformly convex hyperbolic space -- Nonexpansive mapping -- Midpoint rule -- Fixed point -- Condition(A) -- Convergence; 47H09 -- 47H10
• DOI: 10.1016/j.ajmsc.2019.02.002
• Languages: English
• ISSNs: 1319-5166

Abstract

Abstract : The purpose of this paper is to introduce the implicit midpoint rule (IMR) of nonexpansive mappings in 2- uniformly convex hyperbolic spaces and study its convergence. Strong and △ -convergence theorems based on this algorithm are proved in this new setting. The results obtained hold concurrently in uniformly convex Banach spaces, CAT( 0 ) spaces and Hilbert spaces as special cases.