NEW RESULTS IN THE COUPLED FIXED POINT THEORY FOR MULTI-VALUED OPERATORS

In this paper, we will present a coupled fixed problem in b-metric space for the multi-valued operators satisfying a generalized contraction condition of rational type. First part of the paper presents some fixed point theorems for multi-valued operators in ordered b-metric spaces, while in the second part we apply the above mentioned results to the study of the coupled fixed point problem (existence and uniqueness of the solution), under some contraction type conditions of rational type. In the third part, we discuss data dependence, well-posedness, Ulam-Hyers stability and Ostrowski property of the coupled fixed point problem.