A fixed point theorem for generalized $(\psi ,\varphi )$-weak contractions in Branciari type generalized metric spaces

Abstract

In this paper, we obtain a new convergence theorem for fixed points of weak contractions in Branciari type generalized metric spaces under weaker conditions. The proof process of the theorem is new and different from that of other authors. An illustrative example of this theorem is to show how the new conditions extend known results.