Fixed point theorems for M-contraction type maps in partially ordered metric spaces and applications

Abstract

This paper presents hybrid fixed point theorems of Krasnosel’skii type and some nonlinear alternatives of Leray-Schauder type involving sums of two operators in a partially ordered normed linear spaces. The results are applied to functional integral equations that have been considered in Ntouyas and Tsamatos[21] for proving the existence of solutions under certain monotonic conditions blending with the existence of upper or lower solution. Applications are alsogiven to some nonlinear functional initial and boundary value problems ofordinary differential equations for proving the existence results.