A New Monotone Iteration Principle in the Theory of PBVPs of Nonlinear First Order Integro-differential Equations

摘要

In this paper the authors prove the algorithms for the existence as well as approximation of the solutions for a periodic boundary value problem of nonlinear first order ordinary integro-differential equations using the operator theoretic techniques in a partially ordered metric space. The main results rely on the Dhage iteration principle embodied in the.recent hybrid fixed point theorems of Dhage (2014) in a partially ordered normed linear space and the approximations of the solutions of the considered nonlinear integro-differential equations are obtained under weak mixed partial continuity and partial compactness or partial Lipschitz conditions. Our hypotheses and results are also illustrated by some concrete numerical examples. We claim that the approach as well as the results of this paper are new and include some known results for the nonlinear differential equations as special cases.