Document Type : Research Paper

Authors

• Sudheer Petwal ¹
• Anita Tomar ²
• Meena Joshi ³

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

Abstract

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.

Keywords

• Weak P− property
• α-proximal admissible
• partially ordered