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Fixed‐Point Result for Generalized Enriched Contractions With Applications in Cantilever Beam Problem and Homotopy Theory

Author

Listed:
  • Shivani Kukreti
  • Shivam Rawat
  • Mohammad Sajid
  • R. C. Dimri

Abstract

In this study, we introduce a novel class of mappings called orthogonal extended interpolative enriched Ćirić–Reich–Rus type ψF‐contractions and establish fixed‐point results within the framework of orthogonal complete convex extended b‐metric spaces. The unique fixed point is approximated using a Krasnoselskii‐type iterative method. To demonstrate the practical significance of our findings, we present several illustrative examples. Furthermore, recognizing that certain nonlinear systems can be reformulated as integral equations, we validate the applicability of our main results by proving the existence and uniqueness of solution to a Cantilever beam problem. In addition, we extend our analysis to homotopy theory, establishing the existence of a unique solution to related problems.

Suggested Citation

  • Shivani Kukreti & Shivam Rawat & Mohammad Sajid & R. C. Dimri, 2025. "Fixed‐Point Result for Generalized Enriched Contractions With Applications in Cantilever Beam Problem and Homotopy Theory," Journal of Mathematics, John Wiley & Sons, vol. 2025(1).
    • Handle: RePEc:wly:jjmath:v:2025:y:2025:i:1:n:5347383
    DOI: 10.1155/jom/5347383
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    References listed on IDEAS

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    1. Erdal Karapinar & Ravi Agarwal & Hassen Aydi, 2018. "Interpolative Reich–Rus–Ćirić Type Contractions on Partial Metric Spaces," Mathematics, MDPI, vol. 6(11), pages 1-7, November.
    2. Tayyab Kamran & Maria Samreen & Qurat UL Ain, 2017. "A Generalization of b -Metric Space and Some Fixed Point Theorems," Mathematics, MDPI, vol. 5(2), pages 1-7, March.
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