A STUDY OF FIXED POINT THEORY FOR C-CLASS FUNCTIONS WITH APPLICATIONS

Fixed Point Theory is an important branch of non-linear functional analysis. Fixed Point Theorems have applications not only in various branches of mathematics, but also in Economics, Chemistry, Biology, Computer Science, Engineering, and other areas. In recent years, finding a fixed point of contractive type mappings have become the center of strong research activity.In particular, fixed point theorems are used to demonstrate the existence and uniqueness of solutions of differential equations, integral equations, functional equations, partial differential equations and others. Owing to the magnitude, during the past several decades, a large number of generalizations/extensions the Banach Fixed Point Theorem have been explored heavily by many authors. In 2014, the concept of C-class functions was introduced by the Iranian mathematician Ansari [2] which is a pivotal result in the metrical fixed point theory. It should be mentioned that C-class functions cover a large class of contractive conditions.In the present project, we intend to study some aspects of fixed point theory using the properties of C ?class functions or using a number of contraction conditions involving C- class of functions in different types of spaces. We also look for some possible applications of our finding.