Controlled v-generalized metric type space and some fixed point theorems with application

In this article, the concept of controlled v-generalized metric type space is introduced as a generalization of b v (s)-metric spaces and controlled metric type spaces. Some fixed point theorems are proved for Banach orbital contractions and Bianchini type contractions over such spaces. Several examples are given in respect of our new metric type structure and established theorems. In addition, we use our fixed point theorems to find solutions to nonlinear integral equations. AMS subject classification (2020): 47H10; 54H25.