Geometry and Application in Economics of Fixed Point

Abstract

Inspired by the reality that the collection of fixed/common fixed points can embrace any symmetrical geometric shape comparable to a disc, a circle, an elliptic disc, an ellipse, or a hyperbola, we investigate the subsistence of a fixed point and a common fixed point and study their geometry in a partial metric space by introducing some novel contractions and notions of a fixed ellipse-like curve and a common fixed ellipse-like curve which is symmetrical in shape but entirely different than that of an ellipse in a Euclidean space. We look at new hypotheses essential for the collection of nonunique fixed/common fixed points of some mathematical operators to incorporate an ellipse-like curve keeping in view the symmetry in fixed/common fixed points approaches. Appropriate nontrivial examples verify established conclusions. We conclude our work by applying our results to construct the mathematical model and solve the Production–Consumption Equilibrium problem of economics.