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

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.

Authors

B.C. Dhage
(Kasubai, Gurukul Colony, Ahmepur-413515, Dist. Latur, Maharashtra, India)

D. Otrocol
(Tiberiu Popoviciu Institute of Numerical Analysis, Romanian Academy,
Technical University of Cluj-Napoca)

Keywords

Differential equations with maxima; Dhage iteration method; hybrid fixed point theorem; approximation of solutions

Cite this paper as:

B.C. Dhage, D. Otrocol, Dhage iteration method for approximating solutions of nonlinear differential equations with maxima, Fixed Point Theory, 19 (2018) no. 2, pp. 545-556.
DOI: 10.24193/fpt-ro.2018.2.43

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About this paper

Journal

Fixed Point Theory

Publisher Name

House Book Science – Casa Cartii Stiinta, Cluj-Napoca, Romania

Print ISSN

1583-5022

Online ISSN

2066-9208

MR

MR3821782

ZBL

1397.34108

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