Fixed point approximation of nonexpansive mappings and its application to delay integral equation

In this paper, we introduce a modified AG iterative scheme for approximating the fixed point of nonexpansive mappings in a uniformly convex Banach space (UCBS). The convergence and stability are proved for the proposed iterative scheme for the class of Reich–Suzuki nonexpansive mappings. Our results...

Full description

Saved in:
Bibliographic Details
Published inJournal of inequalities and applications Vol. 2025; no. 1; pp. 19 - 17
Main Authors Ishtiaq, Tehreem, Batool, Afshan, Hussain, Aftab, Alsulami, Hamed
Format Journal Article
LanguageEnglish
Published Cham Springer International Publishing 21.02.2025
Springer Nature B.V
SpringerOpen
Subjects
Analysis
Applications of Mathematics
Approximation
Banach spaces
Convergence
Fixed point
Integral equations
Mathematics
Mathematics and Statistics
Modified iteration
Nonexpansive mapping
Partial differential equations
Rate of convergence
η-stability
47H10
47H09
Modified iteration
Rate of convergence
Nonexpansive mapping
stability
Fixed point
Online AccessGet full text

Cover

More Information
Summary:In this paper, we introduce a modified AG iterative scheme for approximating the fixed point of nonexpansive mappings in a uniformly convex Banach space (UCBS). The convergence and stability are proved for the proposed iterative scheme for the class of Reich–Suzuki nonexpansive mappings. Our results generalize many comparable results in the literature. This work shows improved convergence rate, faster iteration, and enhanced convergence efficiency. Finally, we compare our scheme with the Picard, Mann, Noor, Picard–Mann, M, and Thakur iterative schemes with the help of numerical examples that demonstrate faster convergence.
Bibliography:ObjectType-Article-1
SourceType-Scholarly Journals-1
ObjectType-Feature-2
content type line 14
ISSN:1029-242X
1025-5834
1029-242X
DOI:10.1186/s13660-025-03263-0