The implicit midpoint rule for nonexpansive mappings in 2-uniformly convex hyperbolic spaces

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...

Full description

Saved in:
Bibliographic Details
Published inArab journal of mathematical sciences Vol. 26; no. 1/2; pp. 95 - 105
Main Authors Fukhar-ud-din, H., Khan, A.R.
Format Journal Article
LanguageEnglish
Published Bingley Elsevier B.V 31.08.2020
Emerald Group Publishing Limited
Emerald Publishing
Subjects
Banach spaces
Codes
Condition(A)
Convergence
Fixed point
Inequality
Iterative methods
Midpoint rule
Nonexpansive mapping
Uniformly convex hyperbolic space
47H10
Midpoint rule
47H09
Uniformly convex hyperbolic space
Nonexpansive mapping
Condition(A)
Fixed point
Convergence
Online AccessGet full text

Cover

More Information
Summary: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, CAT0 spaces and Hilbert spaces as special cases.
ISSN:1319-5166
2588-9214
DOI:10.1016/j.ajmsc.2019.02.002