Some new theorems for cyclic contractions in Gb-metric spaces and some applications

In this paper, some new theorems for various cyclic contractions are established in G(b)-metric spaces to discuss the existence and uniqueness of the solutions for a class of the operator equations, which generalize many known results in corresponding literatures. On the other hand, we introduce the notion of the cyclic alpha-psi phi-contraction mappings in G(b)-metric spaces and establish a new fixed point theorem, which is applied to consider the existence of the solutions of the integral equations and ordinary differential equations. Moreover, some examples are given to support our main results. (C) 2018 Elsevier Inc. All rights reserved.