Best proximant for set-valued maps via proximal relations

Document Type : Research Paper


1 Government Post Graduate College, Agastyamuni, Uttarakhand-246421, India

2 Pt. L. M. S. Campus, Sridev Suman Uttarakhand University, Rishikesh-249201, India

3 S. S. J. Campus, Soban Singh Jeena Uttarakhand University, Almora-263601, India


We familiarize AM and SAM−contractions involving rational terms to prove the best proximant for discontinuous set-valued maps in partially ordered metric spaces. In the sequel, we demonstrate that completeness of space or subspace is not mandatory for the survival of the best proximant of set-valued maps. Obtained outcomes are unifications, extensions, improvements, and generalizations of some of the widely known results. We provide non-trivial illustrations to exhibit the importance of our explorations.


Volume 14, Issue 1
January 2023
Pages 1237-1247
  • Receive Date: 21 November 2021
  • Revise Date: 06 September 2021
  • Accept Date: 06 October 2022