Fixed point theorems for quadruple self-mappings satisfying integral type inequalities

Abstract

In this paper, we study the generalization of (S; F)-rational contraction pair (h; g) to almost (S; F; Γ)-rational contraction pair (h; g) of integral type on metric spaces and give fixed point results of integral types. For demonstration we give examples which show that our work generalize many results.
There is an important and significant role of fixed point theorems (FPTs) in answering mathematical problems in numerous scientific fields including equilibrium problems, selection and matching problems, image processing,
the study of existence and uniqueness of solutions (EUS) for the integral and differential equations of different classes. Recently, there are a large number new and extended fixed point theorems for the integral inequalities.
In this paper, we generalize the notion of generalized almost (S; F)-rational contraction pair (h; g) to the generalized almost (S; F; Γ)-rational contraction pair (h; g) of integral type and produce some FPT via integral inequalities. This work generalizes many results in the available literature.