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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| Published in | Journal of inequalities and applications Vol. 2025; no. 1; p. 52 |
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| Main Authors | , , |
| Format | Journal Article |
| Language | English |
| Published |
Cham
Springer International Publishing
01.12.2025
Springer Nature B.V |
| Subjects | |
| Online Access | Get full text |
| ISSN | 1025-5834 1029-242X |
| DOI | 10.1186/s13660-025-03298-3 |
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| Abstract | 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. |
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| AbstractList | 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. 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. |
| Author | Shukla, Rahul Anjana Mani, Naveen |
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| Copyright | The Author(s) 2025 Copyright Springer Nature B.V. Dec 2025 |
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| DOI | 10.1186/s13660-025-03298-3 |
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| Snippet | 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... 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... |
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| SubjectTerms | Analysis Applications of Mathematics Boundary value problems Fixed points (mathematics) Graphical representations Mathematics Mathematics and Statistics Metric space Theorems Transverse oscillation |
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| Title | Generalized R - contractions and fixed point theorems with an application to boundary value problem governing transverse oscillation in homogeneous bar |
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