SOME FIXED POINT THEOREMS FOR GENARALIZED α-β-FG-CONTRACTIONS IN b-METRIC SPACES AND CERTAIN APPLICATIONS TO THE INTEGRAL EQUATIONS

Abstract

The purpose of this paper is to introduce a generalized α-β-FGcontraction and prove some fixed point theorems in b-metric spaces. These theorems are generalizations of some results in literature. An example is given to illustrate the obtained results and to show that these results are proper extensions of the existing ones. Then we apply the obtained theorem to study the existence of solutions of the integral equation.