Some Fixed Point Theorems for Orbitally-(p, q)-Quasi-contraction Mappings

Abstract

In this paper, we provide some existence and uniqueness results for a .p; q/-quasi-contraction mapping acting on an orbitally-complete cone metric space. These results generalize several fixed point theorems, in particular those due to Ilić and Rakočević's for quasi-contraction mappings (Ilić and Rakočević, Appl Math Lett 22(5):728-731, 2009), convex contraction mapping, and two-sided convex contraction of order 2.