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Fixed-Point and Random Fixed-Point Theorems in Preordered Sets Equipped with a Distance Metric

Author

Listed:
  • Himanshu Baranwal

    (Department of Mathematics, Indian Institute of Technology Madras, Chennai 600036, India)

  • Ravindra Kishor Bisht

    (Department of Mathematics, National Defence Academy, Pune 411023, India)

  • Arya Kumar Bedabrata Chand

    (Department of Mathematics, Indian Institute of Technology Madras, Chennai 600036, India)

  • Jen-Chih Yao

    (Center for General Education, China Medical University, Taichung 40402, Taiwan
    UNEC Mathematical Modeling and Optimization Research Center, Azerbaijan State University of Economics (UNEC), Istiqlaliyyat Str. 6, Baku 1001, Azerbaijan)

Abstract

This paper explores fixed points for both contractive and non-contractive mappings in traditional b -metric spaces, preordered b -metric spaces, and random b -metric spaces. Our findings provide insights into the behavior of mappings under various constraints and extend our approach to include coincidence and common fixed-point theorems in these spaces. We present new examples and graphical representations for the first time, offering novel results and enhancing several related findings in the literature, while broadening the scope of earlier works of Ran and Reurings, Nieto and Rodríguez-López, Górnicki, and others.

Suggested Citation

  • Himanshu Baranwal & Ravindra Kishor Bisht & Arya Kumar Bedabrata Chand & Jen-Chih Yao, 2024. "Fixed-Point and Random Fixed-Point Theorems in Preordered Sets Equipped with a Distance Metric," Mathematics, MDPI, vol. 12(18), pages 1-30, September.
    • Handle: RePEc:gam:jmathe:v:12:y:2024:i:18:p:2877-:d:1478821
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    References listed on IDEAS

    as
    1. H.K. Xu, 2003. "An Iterative Approach to Quadratic Optimization," Journal of Optimization Theory and Applications, Springer, vol. 116(3), pages 659-678, March.
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