Simulation functions on metric fixed point theory

This paper aims to generalize the primary result of Khojasteh et al. by introducing and expanding the concept of simulation functions and weak ζ -contractions under weaker conditions. The Banach contraction principle is extended using the Kummer test, which generalizes this principle to weak ζ -cont...

Full description

Saved in:
Bibliographic Details
Published inJournal of inequalities and applications Vol. 2025; no. 1; pp. 45 - 17
Main Author Mottaghi Golshan, Hamid
Format Journal Article
LanguageEnglish
Published Cham Springer International Publishing 31.03.2025
Springer Nature B.V
SpringerOpen
Subjects
(Generalized) Simulation function
(Weak) ζ-contraction
Analysis
Applications of Mathematics
Applied mathematics
Approximation
Estimates
Fixed point
Fixed points (mathematics)
Mathematics
Mathematics and Statistics
Posteriori estimate
Priori estimate
Simulation
Weak
47H10
Priori estimate
47H09
(Generalized) Simulation function
contraction
Posteriori estimate
Fixed point
Online AccessGet full text

Cover

More Information
Summary:This paper aims to generalize the primary result of Khojasteh et al. by introducing and expanding the concept of simulation functions and weak ζ -contractions under weaker conditions. The Banach contraction principle is extended using the Kummer test, which generalizes this principle to weak ζ -contractions, providing error estimates for various types of contractions, including Boyd and Wong’s contraction. The results not only offer new findings but also improve and complete several earlier works. Additionally, practical examples are provided to illustrate the applications and demonstrate the necessity of certain assumptions in the theory of metric fixed points.
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/s13660-025-03287-6