Preliminaries on CAT (0) Spaces and Fixed Points of a Class of Iterative Schemes

TL;DR

This paper explores convexity concepts in metric spaces and their relation to fixed points of iterative schemes, providing foundational results for understanding convergence in these spaces.

Contribution

It introduces new connections between convexity properties and iterative mappings in geodesic metric spaces, advancing theoretical understanding.

Findings

Relations between convexity types and fixed point properties

Properties of iterative sequences in convex metric spaces

Insights into convergence behavior of iterative schemes

Abstract

This paper gives some relating results for various concepts of convexity in metric spaces such as midpoint convexity, convex structure, uniform convexity and near-uniform convexity, Busemann curvature and its relation to convexity. Some properties of uniform convexity and near uniform convexity of geodesic metric spaces are related to the mapping built with the concourse of two primary mappings and the associated generated sequences by some iterative schemes.