Document Type : Research Paper
Authors
- Anita Tomar ^{} ^{} ^{1}
- Deepak Kumar ^{} ^{2}
- Ritu Sharma ^{3}
- Meena Joshi ^{} ^{4}
^{1} Department of Mathematics, Pt. L. M. S. Campus, Sridev Suman Uttarakhand University, Rishikesh-249201, Uttarakhand, India.
^{2} Department of Mathematics, Lovely Professional University, Phagwara, Punjab-144411, India.
^{3} G.I.C. Gheradhar (Dogi) Tehri Garhwal (Uttrakhand), India.
^{4} Department of Mathematics, S. S. J. Campus, Soban Singh Jeena University Almora-263601, Uttarakhand, India.
Abstract
We give a method to establish a fixed point via partial $b$-metric for multivalued mappings. Since the geometry of multivalued fixed points perform a significant role in numerous real-world problems and is fascinating and innovative, we introduce the notions of fixed circle and fixed disc to frame hypotheses to establish fixed circle/ disc theorems in a space that permits non-zero self-distance with a coefficient more significant than one. Stimulated by the reality that the fixed point theorem is the frequently used technique for solving boundary value problems, we solve a pair of elliptic boundary value problems. Our developments cannot be concluded from the current outcomes in related metric spaces. Examples are worked out to substantiate the validity of the hypothesis of our results.
Keywords
Main Subjects
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