Abstract In this paper, we improve the Proinov theorem by adding certain rational expressions to definition of corresponding contractions. After that, prove fixed point theorems for these modified contractions in framework dislocated b -metric spaces. We show some illustrative examples indicate validity main results.

The objective of this paper is to describe the concept intuitionistic fuzzy metric-like spaces. This space an extension spaces and metric spaces, We discuss convergence sequences, contractive mapping some fixed-point theorems in space. also give explanations, examples counterexamples validate superiority these results. Our results provide a substantial several important from

Abstract In this article we make an improvement in the Banach contraction using a controlled function metric like spaces, which generalizes many results literature. Moreover, present application on Fredholm type integral equation.