Fixed point results for β − F −weak contraction mappings in complete S-metric spaces

Introduction/purpose: This paper introduces the concept of β − F-weak contraction by using the concepts of F −weak contraction and α − ψ− contraction. Methods: The use of the β − F-weak contraction proves some fixed points theorems in the framework of S−metric spaces. Results: The obtained results on fixed points in S−metric spaces generalize some known results in the literature. Conclusions: The β − F −weak contraction generalizes some important contraction types and examines the existence of a fixed point in S−metric spaces. The results are used to solve a non-linear Fredholm integral equation.