Work

On multi-valued generalized $ \alpha $-nonexpansive mappings and an application to two-point BVPs

Year: 2025

Type: article

Abstract: In recent years, many researchers have studied the fixed points of generalized $ \alpha $-nonexpansive (GAN) mappings, yet there has been limited research on multi-valued GAN mappings. In this paper, we focused on the class of multi-valued GAN mappings in the context of Banach spaces. We introduced a novel iterative process to find fixed points of these mappings and established weak and strong convergence theorems under mild conditions. To demonstrate the numerical efficiency of our new approach, we presented a supportive example and compare the accuracy of our method with existing iteration processes. To show practical usability of the research, we considered a larger class of boundary value problems (BVPs) and proved a convergence result with a supportive example. Our results are new and unify several results of the current literature.

Source: AIMS Mathematics

DOI: 10.3934/math.2025019

Authors: Junaid Ahmad, Imen Ali Kallel, Ahmad Aloqaily, Nabil Mlaiki

Institutions: International Islamic University, Islamabad, Northern Border University, Prince Sultan University, Western Sydney University

Language: English

Topic: Fixed Point Theorems Analysis

Subfield: Geometry and Topology

Field: Mathematics

Domain: Physical Sciences

Open Access status: gold

Estimated APC paid: $1,200

Funder: Prince Sultan University