Successive approximations for a differential equation in a Banach space via Constantin condition-Reference-Cited by-同舟云学术

Successive approximations for a differential equation in a Banach space via Constantin condition

Published:2021-01-29 Issue:1 Volume:71 Page:105-116
ISSN:1337-2211
Container-title:Mathematica Slovaca
language:en
Short-container-title:

Author:

Dutkiewicz Aldona¹,Zima Mirosława²

Affiliation:

1. Faculty of Mathematics and Computer Science, Adam Mickiewicz University in Poznań , Uniwersytetu Poznańskiego 4 , Poznań , Poland

2. Institute of Mathematics , University of Rzeszów , Pigonia 1 , Rzeszów , Poland

Abstract

Abstract We give some sufficient conditions for the convergence of the sequence of successive approximations to the unique solution of first order Cauchy problem in a Banach space. Our approach is based on a generalized Nagumo condition due to A. Constantin and the properties of the Kuratowski measure of noncompactness.

Publisher

Walter de Gruyter GmbH

Subject

General Mathematics

Link

https://www.degruyter.com/document/doi/10.1515/ms-2017-0455/pdf

Reference30 articles.

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3. Athanassov, Z. S.: Uniqueness and convergence of succeessive approximations for ordinary differential equations, Math. Japon. 35 (1990), 351–367.

4. Banaś, J.: Measures of noncompactness in the study of solutions of nonlinear differential and integral equations, Cent. Eur. J. Math. 10 (2012), 2003–2011.

5. Banaś, J.—Goebel, K.: Measures of Noncompactness in Banach Spaces, Marcel Dekker, New York-Basel, 1980.

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