Semi-Hyers-Ulam-Rassias stability for an integro-differential equation of order 𝓃-Reference-Cited by-同舟云学术

Semi-Hyers-Ulam-Rassias stability for an integro-differential equation of order 𝓃

Published:2023-01-01 Issue:1 Volume:56 Page:
ISSN:2391-4661
Container-title:Demonstratio Mathematica
language:en
Short-container-title:

Author:

Inoan Daniela¹,Marian Daniela¹

Affiliation:

1. Department of Mathematics, Technical University of Cluj-Napoca, 28 Memorandumului Street , 400114 , Cluj-Napoca , Romania

Abstract

Abstract The Laplace transform method is applied in this article to study the semi-Hyers-Ulam-Rassias stability of a Volterra integro-differential equation of order n, with convolution-type kernel. This kind of stability extends the original Hyers-Ulam stability whose study originated in 1940. A general integral equation is formulated first, and then some particular cases (polynomial function and exponential function) for the function from the kernel are considered.

Publisher

Walter de Gruyter GmbH

Subject

General Mathematics

Link

https://www.degruyter.com/document/doi/10.1515/dema-2022-0198/pdf

Reference36 articles.

1. S. M. Ulam, A Collection of Mathematical Problems, Interscience, New York, 1960.

2. D. H. Hyers, On the stability of the linear functional equation, Proc. Natl. Acad. Sci. USA 27 (1941), 222–224, DOI: https://doi.org/10.1073/pnas.27.4.222.

3. S. Czerwik, On the stability of the quadratic mapping in normed spaces, Abh. Math. Semin. Univ. Hambg. 62 (1992), 59–64, DOI: https://doi.org/10.1007/BF02941618.

4. T. Trif, On the stability of a functional equation deriving from an inequality of Popoviciu for convex functions, J. Math. Anal. Appl. 272 (2002), 604–616, DOI: https://doi.org/10.1016/S0022-247X(02)00181-6.

5. Y.-H. Lee, S. Jung and M. Th. Rassias. Uniqueness theorems on functional inequalities concerning cubic-quadratic-additive equation, J. Math. Inequal. 12 (2018), no. 1, 43–61, DOI: https://doi.org/10.7153/jmi-2018-12-04.