Application to Lipschitzian and Integral Systems via a Quadruple Coincidence Point in Fuzzy Metric Spaces

Abstract

In this paper, the results of a quadruple coincidence point (QCP) are established for commuting mapping in the setting of fuzzy metric spaces (FMSs) without using a partially ordered set. In addition, several related results are presented in order to generalize some of the prior findings in this area. Finally, to support and enhance our theoretical ideas, non-trivial examples and applications for finding a unique solution for Lipschitzian and integral quadruple systems are discussed.

Some Fixed Point Results in E-Metric Spaces and an Application

“…Over several decades the theory of fixed points has been revealed as a very powerful and important tool in the study of nonlinear phenomena. In particular, fixed point theory has been applied to cope with the solutions to problems in functional equations, ordinary differential equations, integral equations, fractional equations, and more (see [1][2][3][4][5][6][7][8][9]). It has been applied in such diverse fields as biology, chemistry, economics, engineering, game theory, physics, and logic programming.…”

“…This principle has subsequently been developed further, including the presentation of the iteration sequence. In 1975, Kramosil and Michalek [11] considered fuzzy metric space, which is a generalization of typical metric space, and extended the relevant topological concepts, leading to a great many applications in different areas; readers may refer to [9] and the references therein. In 2007, Huang and Zhang [12] introduced cone metric space, which greatly generalizes metric space.…”