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On Generalized (α‐ψ)‐Contraction With Rational Contraction Type on Generalized Metric Space Endowed With the Orthogonal Direct Sum

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Listed:
  • Ghadah Albeladi
  • Saleh Omran

Abstract

This paper explores fixed point theory, focusing on (α‐ψ)‐contraction‐type operators defined on complete generalized metric spaces with an orthogonal direct sum structure. It establishes existence and uniqueness results under these extended contraction conditions. The study further derives new fixed point theorems inspired by and extending the frameworks of Dass–Gupta and Jaggi contractions, contextualizing them within generalized metric spaces with direct sum decompositions. By examining the interplay between the functions α and ψ, these results contribute to a unified theory that bridges and generalizes various contractivity concepts previously studied in metric spaces.

Suggested Citation

  • Ghadah Albeladi & Saleh Omran, 2025. "On Generalized (α‐ψ)‐Contraction With Rational Contraction Type on Generalized Metric Space Endowed With the Orthogonal Direct Sum," Journal of Mathematics, John Wiley & Sons, vol. 2025(1).
    • Handle: RePEc:wly:jjmath:v:2025:y:2025:i:1:n:5157693
    DOI: 10.1155/jom/5157693
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    References listed on IDEAS

    as
    1. Erdal Karapınar & Bessem Samet, 2012. "Generalized 𠜶 - ð Contractive Type Mappings and Related Fixed Point Theorems with Applications," Abstract and Applied Analysis, Hindawi, vol. 2012, pages 1-17, September.
    2. Erdal Karapınar & Bessem Samet, 2012. "Generalized α‐ψ Contractive Type Mappings and Related Fixed Point Theorems with Applications," Abstract and Applied Analysis, John Wiley & Sons, vol. 2012(1).
    3. Klaus Deimling, 1985. "Nonlinear Functional Analysis," Springer Books, Springer, number 978-3-662-00547-7, January.
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