# Convergence analysis of Suzuki’s generalized nonexpansive mappings using the Picard–Abbas iteration process

## TL;DR

This paper studies how a new iteration method works with certain types of mathematical mappings, showing it can effectively find fixed points and offering visual comparisons.

## Contribution

The paper introduces convergence results for Suzuki’s nonexpansive mappings using the Picard–Abbas iteration and provides visual insights via polynomiographs.

## Key findings

- Weak and strong convergence results are established for Suzuki’s generalized nonexpansive mappings.
- A numerical example demonstrates the effectiveness of the Picard–Abbas iteration process.
- Polynomiographs reveal visual advantages of the proposed method over existing ones.

## Abstract

This manuscript investigates the convergence behavior of Suzuki’s generalized nonexpansive mappings using the recently introduced Picard–Abbas iteration process. We establish both weak and strong convergence results for the associated fixed-point approximations. To demonstrate the effectiveness of our approach, a numerical example is provided. Furthermore, we generate polynomiographs based on the proposed iteration process and compare them with those produced by existing methods, highlighting the advantages and visual insights offered by our scheme.