Study of Fixed Point Theorems in Fuzzy Metric Spaces

Abstract

Fixed point theorems are the most important tools for providing existence and uniqueness of the solution of various mathematics models (different, integral, partial differential equation and variational inequalities) representing different phenomena suitable for different fields such as steady state temperature distribution, chemical reaction, neutron transport theory, economic theories, epidemics and flow of fluids. At present this field has been recognized as one of the active field of research.
Fixed point theorems is one of the most fruitful and effective tools in mathematics which has enormous applications within as well as outside the mathematics. Despite noted improvements in computer skill and its remarkable success in facilitating many areas of research, there will stands one major short coming: computers are not designed to handle situations wherein uncertainties are involved. To deal with uncertainty. We need techniques other than classical ones wherein some specific logic is required.