Dhage iteration method for approximating solutions of nonlinear differential equations with maxima


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	Dhage iteration method for approximating solutions of nonlinear differential equations with maxima


	Fixed Point Theory, Volume 19, No. 2, 2018, 545-556, June 1st, 2018 DOI: 10.24193/fpt-ro.2018.2.43 Authors: Bapurao C. Dhage and Diana Otrocol Abstract: In this paper we study the initial value problem of first order nonlinear differential equations with maxima and discuss the existence and approximation of the solutions. The main result relies on the Dhage iteration method embodied in a recent hybrid fixed point theorem of Dhage (2014) in a partially ordered normed linear space. At the end, we give an example to illustrate the hypotheses and applicability of the abstract results of this paper. Key Words and Phrases: Differential equations with maxima, Dhage iteration method, hybrid fixed point theorem, approximation of solutions. 2010 Mathematics Subject Classification: 34A12, 34A45, 47H07, 47H10. Published on-line: June 1st, 2018. Abstract pdf Fulltext pdf Back to volume's table of contents