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In this paper, the author proves the existence as well as approximation of the solutions for an initial value problem of first order ordinary nonlinear hybrid differential equations with maxima. An algorithm for the solutions is developed and it is shown that certain sequence of successive approximations converges monotonically to the solution of the related hybrid differential equations under some suitable mixed hybrid conditions. We base our results on the Dhage iteration principle embodied in a recent hybrid fixed point theorem of Dhage (2014) in a partially ordered normed linear space. An example is also provided to illustrate the hypotheses and abstract theory developed in this paper.
How to Cite this article:
Bapurao C. Dhage, Dhage iteration method for nonlinear first order ordinary hybrid differential equations with mixed perturbation of second type and maxima, Journal of Nonlinear Functional Analysis 2016 (2016), Article ID 31.