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Single and Multi-Valued Ordered-Theoretic Perov Fixed-Point Results for θ -Contraction with Application to Nonlinear System of Matrix Equations

Author

Listed:
  • Fahim Ud Din

    (Abdus Salam School of Mathematical Sciences, Governement College University, Lahore 54600, Pakistan)

  • Salha Alshaikey

    (Mathematics Department, Al-Qunfudah University College, Umm Al-Qura University, Mecca 21421, Saudi Arabia)

  • Umar Ishtiaq

    (Office of Research, Innovation and Commercialization, University of Management and Technology, Lahore 54770, Pakistan)

  • Muhammad Din

    (Abdus Salam School of Mathematical Sciences, Governement College University, Lahore 54600, Pakistan)

  • Salvatore Sessa

    (Dipartimento di Architettura, Università Dinapoli Federico II, Via Toledo 403, 80121 Napoli, Italy)

Abstract

This paper combines the concept of an arbitrary binary connection with the widely recognized principle of θ -contraction to investigate the innovative features of vector-valued metric spaces. This methodology demonstrates the existence of fixed points for both single- and multi-valued mappings within complete vector-valued metric spaces. Through the utilization of binary relations and θ -contraction, this study advances and refines the Perov-type fixed-point results in the literature. Furthermore, this article furnishes examples to substantiate the validity of the presented results. Additionally, we establish an application for finding the existence of solutions to a system of matrix equations.

Suggested Citation

  • Fahim Ud Din & Salha Alshaikey & Umar Ishtiaq & Muhammad Din & Salvatore Sessa, 2024. "Single and Multi-Valued Ordered-Theoretic Perov Fixed-Point Results for θ -Contraction with Application to Nonlinear System of Matrix Equations," Mathematics, MDPI, vol. 12(9), pages 1-15, April.
    • Handle: RePEc:gam:jmathe:v:12:y:2024:i:9:p:1302-:d:1382770
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