Coupled fixed point results for (ϕ,G)-contractions of type (b) in b-metric spaces endowed with a graph

The purpose of this paper is to present some existence results for coupled fixed points of generalized contraction type operators in b-metric spaces endowed with a directed graph. Our results generalize the results obtained by Gnana Bhaskar and Lakshmikantham in [T. Gnana Bhaskar, V. Lakshmikantham, Nonlinear Anal., 65 (2006), 1379–1393]. Data dependence, well-posednes and Ulam-Hyres stability of the fixed point problem are also studied.