Convergence of Iterative Algorithms in Cat(0) Spaces

Noor Saddam Taresh,Shaimaa S Albundi,Salwa Salman Abed

doi:10.24996/ijs.2022.63.1.24

Abstract

In this article, results have been shown via using a general quasi contraction multi-valued mapping in Cat(0) space. These results are used to prove the convergence of two iteration algorithms to a fixed point and the equivalence of convergence. We also demonstrate an appropriate conditions to ensure that one is faster than others.

Highlights

Introduction and PreliminariesAxiomatically, in a cat (k) triangles are slimmer than corresponding triangles in a usual space of fixed curvature k
After the Kannan’s theorem established, many studies were devoted to obtain other fixed point results for various types of contractive conditions that do not require the continuity of
The following contractive condition has been mentioned in the [13], for single valued mappings in metric space case, we present the contractive condition for multivalued mappings in Cat (0) spaces

Summary

Introduction

Introduction and PreliminariesAxiomatically, in a cat (k) triangles are slimmer than corresponding triangles in a usual space of fixed curvature k. Let be a metric space and Definition 1.1: [2] A geodesic path from such as (geodesic path joining u to v) is an isometry In is a Definition 1.4: [1] A geodesic space is named CAT(0) space if whole geodesic triangles accomplish the following comparison axiom. Lemma gives the definition of CN inequality that is found in [4].

Objectives

Results

Conclusion