Nonlinear contractions involving simulation functions in a metric space with a partial order

Abstract

Very recently, Khojasteh, Shukla and Radenovic [F. Khojasteh, S. Shukla, S. Radenovic, Filomat, 29 (2015), 1189-1194] introduced the notion of Z-contraction, that is, a nonlinear contraction involving a new class of mappings namely simulation functions. This kind of contractions generalizes the Banach contraction and unifies several known types of nonlinear contractions. In this paper, we consider a pair of nonlinear operators satisfying a nonlinear contraction involving a simulation function in a metric space endowed with a partial order. For this pair of operators, we establish coincidence and common fixed point results. As applications, several related results in fixed point theory in a metric space with a partial order are deduced.