Generalized R - contractions and fixed point theorems with an application to boundary value problem governing transverse oscillation in homogeneous bar

We introduce the notion of generalized R - contractions for single self-maps via w - distance in relational-theoretic metric space. We utilized this notion to find the existence and uniqueness of a fixed point for self-map using the locally Ψ-transitivity property. In order to validate our findings,...

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Bibliographic Details
Published inJournal of inequalities and applications Vol. 2025; no. 1; p. 52
Main Authors Mani, Naveen, Anjana, Shukla, Rahul
Format Journal Article
LanguageEnglish
Published Cham Springer International Publishing 01.12.2025
Springer Nature B.V
Subjects
Analysis
Applications of Mathematics
Boundary value problems
Fixed points (mathematics)
Graphical representations
Mathematics
Mathematics and Statistics
Metric space
Theorems
Transverse oscillation
connected
47H10
Oscillation
Binary relation
contractions
Homogeneous bar
54H25
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Summary:We introduce the notion of generalized R - contractions for single self-maps via w - distance in relational-theoretic metric space. We utilized this notion to find the existence and uniqueness of a fixed point for self-map using the locally Ψ-transitivity property. In order to validate our findings, some examples with graphical representation are also presented. At last, we incorporate this work with an application to find the existence of solution to a forth order boundary value problem governing transverse oscillation in a homogeneous bar.
Bibliography:ObjectType-Article-1
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ISSN:1025-5834
1029-242X
DOI:10.1186/s13660-025-03298-3