Approximating Solutions of Non Linear First Order Abstract Measure Differential Equations by Using Dhage Iteration Method
Applied and Computational Mathematics
Volume 9, Issue 3, June 2020, Pages: 64-69
Received: Apr. 15, 2020;
Accepted: Apr. 30, 2020;
Published: Jun. 4, 2020
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Dnyanoba Maroti Suryawanshi, Dayanand Science College Latur, Swami Ramanand Teerth Marathwada University, Nanded, India
Sidheshwar Sangram Bellale, Dayanand Science College Latur, Swami Ramanand Teerth Marathwada University, Nanded, India
Pratiksha Prakash Lenekar, Dayanand Science College Latur, Swami Ramanand Teerth Marathwada University, Nanded, India
In this paper we have proved the approximating solutions of the nonlinear first order abstract measure differential equation by using Dhage’s iteration method. The main result is based on the iteration method included in the hybrid fixed point theorem in a partially ordered normed linear space. Also we have solved an example for the applicability of given results in the paper. Sharma  initiated the study of nonlinear abstract differential equations and some basic results concerning the existence of solutions for such equations. Later, such equations were studied by various authors for different aspects of the solutions under continuous and discontinuous nonlinearities. The study of fixed point theorem for contraction mappings in partial ordered metric space is initiated by different authors. The study of hybrid fixed point theorem in partially ordered metric space is initiated by Dhage with applications to nonlinear differential and integral equations. The iteration method is also embodied in hybrid fixed point theorem in partially ordered spaces by Dhage . The Dhage iteration method is a powerful tool for proving the existence and approximating results for nonlinear measure differential equations. The approximation of the solutions are obtained under weaker mixed partial continuity and partial Lipschitz conditions. In this paper we adopted this iteration method technique for abstract measure differential equations.
Dnyanoba Maroti Suryawanshi,
Sidheshwar Sangram Bellale,
Pratiksha Prakash Lenekar,
Approximating Solutions of Non Linear First Order Abstract Measure Differential Equations by Using Dhage Iteration Method, Applied and Computational Mathematics.
Vol. 9, No. 3,
2020, pp. 64-69.
Copyright © 2020 Authors retain the copyright of this article.
This article is an open access article distributed under the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0/
) which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
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