Existence and convergence theorems for monotone generalized alpa-nonexpansive mappings in uniformly convex partially ordered hyperbolic metric spaces and its application

TL;DR

This paper extends existence and convergence theorems for monotone generalized alpha-nonexpansive mappings in uniformly convex partially ordered hyperbolic metric spaces, demonstrating faster convergence and applying results to integral equations.

Contribution

It generalizes previous existence results and proves convergence theorems for iterative schemes in a broader class of hyperbolic metric spaces.

Findings

The iterative scheme converges faster than previous methods.

The results are applicable to solving integral equations.

The paper provides a numerical example illustrating improved convergence.

Abstract

In this paper, we generalize the existence result in [14] and prove convergence theorems of the iterative scheme in [12, 16] for monotone generalized alpa-nonexpansive mappings in uniformly convex partially ordered hyperbolic metric spaces. And we also give a numerical example to show that this scheme converges faster than the scheme in [14] and apply the result to the integral equation.