Application to fixed point theory of -Geraghty Pata proximal contractions

In this paper, we introduce the concepts of -Geraghty Pata proximal contractions and their weak ϕ -variants, which generalize and unify several well-known contraction conditions in fixed point theory. By integrating the ideas of Geraghty and Pata contractions with the framework of α − θ -proximal ad...

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Bibliographic Details
Published in:Fixed point theory and algorithms for sciences and engineering Vol. 2025; no. 1; pp. 19 - 24
Main Authors: Alam, Khairul Habib, Rohen, Yumnam, Albargi, Amer Hassan, Hussain, Aftab
Format: Journal Article
Language:English
Published: Cham Springer International Publishing 01.12.2025
Springer Nature B.V
SpringerOpen
Subjects:
Analysis
Applications of Mathematics
Approximation
Differential equations
Differential Geometry
Fixed points (mathematics)
Fractional calculus
Geraghty Pata proximal contraction
Geraghty Pata type coupled fixed point
Mapping
Mathematical and Computational Biology
Mathematics
Mathematics and Statistics
Metric space
Theorems
Topology
Weak -Geraghty Pata proximal contraction
α − θ $\alpha -\theta $ -proximal admissibility
Weak
47H10
54E50
46T99
Geraghty Pata proximal contraction
Geraghty Pata type coupled fixed point
54H10
proximal admissibility
ISSN:2730-5422
Online Access:Get full text
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Summary:In this paper, we introduce the concepts of -Geraghty Pata proximal contractions and their weak ϕ -variants, which generalize and unify several well-known contraction conditions in fixed point theory. By integrating the ideas of Geraghty and Pata contractions with the framework of α − θ -proximal admissibility, we establish best proximity point theorems for both single-valued and multivalued non-self mappings in metric spaces. Furthermore, we extend our results to the context of coupled fixed points and partially ordered metric spaces, thus broadening their applicability. The presented theorems generalize a range of existing results and offer a more flexible setting for analyzing nonlinear problems. We also include a concrete application to fractional differential equations and provide illustrative examples to demonstrate the effectiveness of our results.
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ISSN:2730-5422
DOI:10.1186/s13663-025-00799-0