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On new stability results for composite functional equations in quasi-β-normed spaces

Thanyacharoen Anurak, Sintunavarat Wutiphol

Demonstratio Mathematica

2021

Vol. 54, nr 1

68--84

In this article, we prove the generalized Hyers-Ulam-Rassias stability for the following composite functional equation: f(f(x) – f(y)) = f(x + y) + f(x – y) – f(x) – f(y), where f maps from a(β, p)-Banach space into itself, by using the fixed point method and the direct method. Also, the generalized Hyers-Ulam-Rassias stability for the composite s-functional inequality is discussed via our results.

Ulam-Hyers stability of a parabolic partial differential equation

Marian Daniela, Ciplea Sorina Anamaria, Lungu Nicolaie

Demonstratio Mathematica

2019

Vol. 52, nr 1

475--481

The goal of this paper is to give an Ulam-Hyers stability result for a parabolic partial differential equation. Here we present two types of Ulam stability: Ulam-Hyers stability and generalized Ulam-Hyers-Rassias stability. Some examples are given, one of them being the Black-Scholes equation.

Stability of n-dimensional additive functional equation in generalized 2-normed space

Arunkumar M.

Demonstratio Mathematica

2016

Vol. 49, nr 3

319--330

In this paper, the author established the general solution and generalized Ulam–Hyers–Rassias stability ofn-dimensional additive functional equation (…) in generalized 2-normed space.