Coupled fixed points for mixed monotone condensing operators and an existence theorem of the solutions for a class of functional equations arising in dynamic programming

AbstractIn this paper, the existence and iterative approximation of coupled fixed points for mixed monotone condensing (set-valued) operators are discussed. The results presented here extend and improve the corresponding results of [D. Guo and V. Lakshmikantham, coupled fixed points of nonlinear operators [1, 2]. As an application, we utilize the results obtained in Section 2 to study the existence problem of solutions for a class of functional equations arising in dynamic programming