University of MaraghehSahand Communications in Mathematical Analysis2322-580720420230901Results via Partial-$b$ Metric and Solution of a Pair of Elliptic Boundary Value Problem20522570671010.22130/scma.2023.563638.1187ENAnitaTomarDepartment of Mathematics, Pt. L. M. S. Campus, Sridev Suman Uttarakhand University, Rishikesh-249201, Uttarakhand, India.0000-0001-8033-856XDeepakKumarDepartment of Mathematics,
Lovely Professional University, Phagwara, Punjab-144411, India.0000-0002-1028-5594RituSharmaG.I.C. Gheradhar (Dogi) Tehri Garhwal (Uttrakhand), India.MeenaJoshiDepartment of Mathematics, S. S. J. Campus, Soban Singh Jeena University Almora-263601, Uttarakhand, India.0000-0002-1562-0988Journal Article20221017We 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.https://scma.maragheh.ac.ir/article_706710_c0125cadcfcb02e00975836a6597f88a.pdf