Abstract
In this paper, we prove algorithms for the existence as well as the approximation of solutions to initial value problems (IVPs) for nonlinear first order ordinary integrodifferential equations using operator theoretic techniques in a partially ordered metric space. The main results rely on the Dhage iteration method embodied in the recent hybrid fixed point theorems of Dhage in a partially ordered normed linear space. The approximations to the solutions are obtained under weaker mixed partial continuity and Lipschitz conditions. The hypotheses and results are also illustrated by some examples.
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Dhage, B.C., Dhage, S.B. & Graef, J.R. Dhage iteration method for initial value problems for nonlinear first order hybrid integrodifferential equations. J. Fixed Point Theory Appl. 18, 309–326 (2016). https://doi.org/10.1007/s11784-015-0279-3
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DOI: https://doi.org/10.1007/s11784-015-0279-3