A Study of Fixed Point Theorem in Metric Spaces

Exploring common fixed-point theorems and their applications in mathematics and economics

Abstract

In this study, it is shown that the fixed-point theory is best approximated and the variation inequality results are best approximated. The change of inequality results in a theory of fixed points. It is also 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 certain desired 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 first mathematician to show that solutions of nonlinear equations existed and existed under certain conditions. Banach's fixed point theorems have become a key feature in functional analysis history. The Banach contraction principle has many applications and has spread over nearly all mathematical branches.In the study of problems of the common fixed points of non-commuting mapping, the notion of compatibility plays an important role. In addition, the continuity of one of the mapping process is compulsorily required when obtaining a common fixed point in the orems. The present study aims to achieve a reciprocal continuity of common fixed-point theorems. Finally, the existence and uniqueness of common solutions in the dynamic programming for the functional equations has been tested.