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Reich Graph Contraction in Graphically Extended b‐Metric Spaces With Applications to Cantilever Beam Equation

Author

Listed:
  • Azham Ilyass
  • Naveen Mani
  • Rahul Shukla

Abstract

The main focus in this article is to prove the existence and uniqueness of fixed point satisfying Reich graph contraction within the graph structure, in the context of the graphical extended b‐metric spaces. Our findings represent substantial expansions and broader generalizations of certain pioneering results within the current theoretical framework. In order to reinforce the novel outcomes, we put forth some examples utilizing directed graphs. These examples contribute to a better understanding of the results and enhancing the overall clarity of the established result. Furthermore, as an application of our findings, the existence and uniqueness of the solution for the boundary value problem representing the bending of an elastic beam is presented.

Suggested Citation

  • Azham Ilyass & Naveen Mani & Rahul Shukla, 2025. "Reich Graph Contraction in Graphically Extended b‐Metric Spaces With Applications to Cantilever Beam Equation," Journal of Applied Mathematics, John Wiley & Sons, vol. 2025(1).
    • Handle: RePEc:wly:jnljam:v:2025:y:2025:i:1:n:6650209
    DOI: 10.1155/jama/6650209
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    References listed on IDEAS

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    1. 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.
    2. Maria Samreen & Tayyab Kamran & Naseer Shahzad, 2013. "Some Fixed Point Theorems in b‐Metric Space Endowed with Graph," Abstract and Applied Analysis, John Wiley & Sons, vol. 2013(1).
    3. Federico Echenique, 2005. "A short and constructive proof of Tarski’s fixed-point theorem," International Journal of Game Theory, Springer;Game Theory Society, vol. 33(2), pages 215-218, June.
    4. Maria Samreen & Tayyab Kamran & Naseer Shahzad, 2013. "Some Fixed Point Theorems in -Metric Space Endowed with Graph," Abstract and Applied Analysis, Hindawi, vol. 2013, pages 1-9, October.
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