A simpler and more efficient fixed point iterative scheme

TL;DR

This paper introduces a new fixed point iterative scheme that improves convergence speed and efficiency for nonexpansive mappings, supported by theoretical convergence proofs and numerical comparisons.

Contribution

The paper proposes a novel iterative algorithm that enhances convergence efficiency for fixed point problems, with proven convergence properties and superior numerical performance.

Findings

Faster convergence rate than existing methods

Proven weak and strong convergence under certain conditions

Numerical experiments confirm computational advantages

Abstract

Our work presents a new iterative scheme to approximate the fixed points of nonexpansive mapping. The proposed algorithm is constructed to enhance convergence efficiency while preserving theoretical robustness. Under appropriate assumptions on the underlying operator, we establish weak convergence and strong convergence results for the generated sequence. To demonstrate the effectiveness of the proposed scheme, we present a numerical example and perform a detailed comparative study with several well-known iterative methods from the literature. The numerical results clearly indicate that the proposed method exhibits a faster rate of convergence than the existing schemes, thereby confirming its computational advantage. These findings suggest that the new iterative process provides an efficient and reliable alternative for solving fixed point problems arising in applied mathematics and related fields.