Some fixed point results in semi-metric space

Abstract

Mathematics is the backbone of modern science as it deals with the study of quantity structure and shapes. It is remarkably e_cient source of new concepts and tools to provide solution to existing problem. From di_erent perspective, mathematics can be de_ned as a science which involves logical reasoning based on accepted rules, laws and facts. In mathematics, analysis plays a vital role for its development. The study of several functions come under the functional analysis. Functional analysis has been divided into two parts namely linear functional analysis and non-linear functional analysis. Since 1960, _xed point theory is considered to be the part of non-linear func- tional analysis. Functional analysis is an abstract branch of mathematics that originated from classical analysis. It serves as an essential tool for vari- ous branches of mathematical analysis and its applications. Polish mathematician Stephan Banach published his contraction principle in 1922. Since then, this principle has been extended and generalized in several ways. Its development started about eighty years ago and nowadays functional analystic methods and results are important in various _elds of mathematics and its applications. The theory of _xed point is very extensive _eld which has wide applications. Fixed point theory has played a central role in the problems of non-linear functional analysis and provided a power tool in demonstrating the existence and uniqueness of solutions to various math- ematical models representing phenomena arising in di_erent _elds such as in Engineering, Economics , Game Theory and Nash Equilibrium, Steady State Temperature Distribution, Epidemics, Flow of Fluids, Chemical Reactions, Neutron Transport Theory, Haar Measures, Abstract Elliptic Problems. In- variant Subspace Problems, Approximation Problems. French mathematician Maurice Frechet introduced the concept of metric space in 1906. After 22 years from this, Austrian mathematician Karl Menger introduced semi-metric space as an important generalization of metric space.