Results via Partial-b Metric and Solution of a Pair of Elliptic Boundary Value Problem

We give a method to establish a fixed point via partialmetric for multivalued mappings. Since the geometry of multival-ued fixed points perform a significant role in numerous real-world problems and is fascinating and innovative, we introduce the no-tions 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 con-cluded from the current outcomes in related metric spaces. Exam-ples are worked out to substantiate the validity of the hypothesis of our results. We give a method to establish a fixed point via partial.