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Further results on Ulam stability for a system of first-order nonsingular delay differential equations

Zada Akbar, Pervaiz Bakhtawar, Alzabut Jehad, Shah Syed Omar

Demonstratio Mathematica

2020

Vol. 53, nr 1

225--235

This paper is concerned with a system governed by nonsingular delay differential equations. We study the β-Ulam-type stability of the mentioned system. The investigations are carried out over compact and unbounded intervals. Before proceeding to the main results, we convert the system into an equivalent integral equation and then establish an existence theorem for the addressed system. To justify the application of the reported results, an example along with graphical representation is illustrated at the end of the paper.

Stability of an AQCQ functional equation in non-Archimedean (n, β)-normed spaces

Liu Yachai, Yang Xiuzhong, Liu Guofen

Demonstratio Mathematica

2019

Vol. 52, nr 1

130--146

In this paper, we adopt direct method to prove the Hyers-Ulam-Rassias stability of an additive-quadratic-cubic-quartic functional equation f(x+2y)+f(x-2y) = 4f(x+y)+4f(x-y)-6f(x)+f(2y)+f(-2y)-4f(y)-4f(-y) in non-Archimedean (n,β)-normed spaces.

Note on the stability of the system of functional equations

Adam M.

Silesian Journal of Pure and Applied Mathematics

2017

Vol. 7, iss. 1

93--98

We deal with the system of functional equations connected with additive and quadratic mappings. We correct some mistakes made in the paper [W. Fechner, On the Hyers-Ulam stability of functional equations connected with additive and quadratic mappings, J. Math. Anal. Appl. 322 (2006), 774–786] and provide accurate statements of those results. Moreover, we get the improvement of the Hyers-Ulam stability result of the considered system of functional equations.