On fixed point theorems in modular spaces characterized by $C^*$-class functions

Abstract

Generally, finding a solution to a theoretical mathematical modelling problem is equivalent to finding a fixed point for a suitable operator. Accordingly, fixed point theory is therefore a very important and crucial in many areas, such as mathematics, sciences, and engineering. A very popular and important fixed point theory is those formulated by Stefan Banach in 1922. The theory is related to a complete normed space and known as the Banach fixed point theory. Recently there have been numerous generalization of the Banach fixed point theory. One of them is a fixed point theory in modular spaces. In this paper, we will formulate some fixed point theorems in modular spaces by using $C^*$-class functions. The obtained results generalize and improve some results in [Supama, On Some Common Fixed Point Theorems inModulared Spaces, International Mathematical Forum, Vol. 7, no. 52, (2012), 2571 - 2579.].