Generalized α−ψ Rational-Type Contractions and Related Fixed Point Results in Controlled Metric Spaces

We introduce the new notion of generalized α−ψ rational type contractions of type I and type II in controlled metric spaces. By making use of these new notions, some fixed point theorems are also proved in the mentioned spaces for the α− admissible self maps. Some examples on the finite sets are also provided to prove the validity of our results. Some results which are direct consequences of the proved results are mentioned in the form of corollaries. As an application, an integral equation is solved with the aid of our results. Finally, a series electric circuit problem in the form of second-order differential equation is solved by converting it into fixed point problem with the aid of the proved result.