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

Himanshu Baranwal, Ravindra Kishor Bisht, Arya Kumar Bedabrata Chand and Jen-Chih Yao ()
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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

Mathematics, 2024, vol. 12, issue 18, 1-30

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.

Keywords: asymptotic regularity; b -metric space; fixed point; Kannan mapping; monotone mapping; Dottie number; preordered space; random fixed point (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2024
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