Some fixed point results for a generalized ψ-weak contraction mappings in orbitally metric spaces

Samet and Vetro [Samet B, Vetro C. Berinde mappings in orbitally complete metric spaces. Chaos Solitons Fract 2011;44:1075–9.] studied a fixed point theorem for a self-mapping satisfying a general contractive condition of integral type in orbitally complete metric spaces. In this paper, we introduce the notion of a generalized ψ-weak contraction mapping and establish some results in orbitally complete metric spaces. Our results generalize several well-known comparable results in the literature. As an application of our results we deduce the result of Samet and Vetro. Some examples are given to illustrate the useability of our results.