A Study on Fixed Point Theorem of Contraction Mapping Principle in Metric Spaces

Exploring fixed-point theory and its applications in economics and mathematical analysis

Abstract

In this study, it is shown that the fixed-point theory is best approximated and the variationinequality results are best approximated. The change of inequality results in a theory of fixed points. It isalso shown to be the maximum element in mathematical economics for the fixed-point theory. Ultimately,some earlier results have been proved. We need to discuss the existence of solutions with certaindesired properties in many of the problems arising from models of chemical reactors, neutron transport,population biology, infectious diseases, economies and other systems. Banach (1922) was the firstmathematician to show that solutions of nonlinear equations existed and existed under certainconditions. Banach's fixed point theorems have become a key feature in functional analysis history. TheBanach contraction principle has many applications and has spread over nearly all mathematicalbranches.In the study of problems of the common fixed points of non-commuting mapping, the notion ofcompatibility plays an important role. In addition, the continuity of one of the mapping process iscompulsorily required when obtaining a common fixed point in the orems. The present study aims toachieve a reciprocal continuity of common fixed-point theorems. Finally, the existence and uniquenessof common solutions in the dynamic programming for the functional equations has been tested.