Results 31 to 40 of about 814 (188)

On Hyers–Ulam–Rassias Stability of the Pexider Equation

Journal of Mathematical Analysis and Applications, 1999
Let \((G,+)\) be an abelian group, \((X,\|\cdot\|)\) be a Banach space and \(f,g,h:G\rightarrow X\) be mappings. An equation \(f(x+y)=g(x)+h(y)\) is called a Pexider functional equation. In the paper the stability of that equation in the spirit of Hyers-Ulam-Rassias is considered. The main theorem is the following: Let \(\varphi:G\times G\rightarrow[0,\
Dong-Soo Shin, Byung-Do Kim, Kil-Woung Jun   +2 more
openaire   +3 more sources

Asymptotic stability of non‐instantaneous impulsive systems and T‐S fuzzy non‐instantaneous impulsive control for nonlinear systems

IET Control Theory &Applications, Volume 17, Issue 9, Page 1184-1202, 11 June 2023., 2023
Abstract This paper studies the asymptotic stability for a class of non‐instantaneous impulsive systems and Takagi‐Sugeno (T‐S) fuzzy non‐instantaneous impulsive control for linear and nonlinear systems. First, a class of concrete comparison system for a more accurate and universal nonlinear non‐instantaneous impulsive model is constructed.
Hao Deng, Chuandong Li, Yinuo Wang
wiley   +1 more source

A NOTE ON THE HYERS-ULAM-RASSIAS STABILITY OF A QUADRATIC EQUATION [PDF]

Bulletin of the Korean Mathematical Society, 2004
The authors consider two functional equations of quadratic type and give some interesting results concerning their stability in the spirit of papers of the reviewer [J. Math. Anal. Appl. 184, 431--436 (1994; Zbl 0818.46043)] and \textit{W. Jian} [J. Math. Anal. Appl. 263, 406--423 (2001; Zbl 0993.39024)].
Jie-Hyung Kang, Yang-Hi Lee, Chang-Ju Lee   +2 more
openaire   +3 more sources

Equivalence for Various Forms of Quadratic Functional Equations and Their Generalized Hyers–Ulam–Rassias Stability

International Journal of Mathematics and Mathematical Sciences, Volume 2023, Issue 1, 2023., 2023
In this manuscript, we study the properties and equivalence results for different forms of quadratic functional equations. Using the Brzdȩk and Ciepliński fixed‐point approach, we investigate the generalized Hyers–Ulam–Rassias stability for the 3‐variables quadratic functional equation in the setting of 2‐Banach space.
Ravinder Kumar Sharma, Sumit Chandok, Bikash Koli Dey   +2 more
wiley   +1 more source

Semi-Hyers–Ulam–Rassias Stability of the Convection Partial Differential Equation via Laplace Transform

Mathematics, 2021
In this paper, we study the semi-Hyers–Ulam–Rassias stability and the generalized semi-Hyers–Ulam–Rassias stability of some partial differential equations using Laplace transform. One of them is the convection partial differential equation.
Daniela Marian
doaj   +1 more source

On the E‐Hyperstability of the Inhomogeneous σ‐Jensen’s Functional Equation on Semigroups

Abstract and Applied Analysis, Volume 2023, Issue 1, 2023., 2023
In this paper, we study the hyperstability problem for the well‐known σ‐Jensen’s functional equation f(xy) + f(xσ(y)) = 2f(x) for all x, y ∈ S, where S is a semigroup and σ is an involution of S. We present sufficient conditions on E⊂ℝ+S2 so that the inhomogeneous form of σ‐Jensen’s functional equation f(xy) + f(xσ(y)) = 2f(x) + φ(x, y) for all x, y ...
M. Sirouni, S. Kabbaj, Victor Kovtunenko
wiley   +1 more source

Hyers–Ulam–Rassias Stability of an Equation of Davison

Journal of Mathematical Analysis and Applications, 1999
Let \(E_1\) be a normed algebra with a unit element, \(E_2\) be a Banach space and let \(f:E_1\rightarrow E_2\). In the paper the Hyers-Ulam-Rassias stability of the Davison functional equation \[ f(xy)+f(x+y)=f(xy+x)+f(y) \] is proved. As a consequence of the main theorem the authors obtain among others the following: Let \(\varepsilon\geq 0\) and \(p\
Prasanna K. Sahoo, Soon-Mo Jung
openaire   +3 more sources

Some Remarks Concerning the General Octic Functional Equation

Journal of Mathematics, Volume 2023, Issue 1, 2023., 2023
In this article, we study the stability of various forms for the general octic functional equation ∑i=099Ci−19−ifx+iy=0. We first find a special way of representing a given mapping as the sum of eight mappings. And by using the above representation, we will investigate the hyperstability of the general octic functional equation.
Yang-Hi Lee, Jaiok Roh, Gaetano Luciano
wiley   +1 more source

Existence and Ulam–Hyers stability for Caputo conformable differential equations with four-point integral conditions

Advances in Difference Equations, 2019
In this article, we investigate the existence and uniqueness of solutions for conformable derivatives in the Caputo setting with four-point integral conditions, applying standard fixed point theorems such as Banach contraction mapping principle ...
Aphirak Aphithana, Sotiris K. Ntouyas, Jessada Tariboon   +2 more
doaj   +1 more source

Existence and stability results for ψ-Hilfer fractional integro-differential equation with mixed nonlocal boundary conditions

AIMS Mathematics, 2021
In this paper, we discuss the existence, uniqueness and stability of boundary value problems for $\psi$-Hilfer fractional integro-differential equations with mixed nonlocal (multi-point, fractional derivative multi-order and fractional integral ...
Weerawat Sudsutad, Chatthai Thaiprayoon, Sotiris K. Ntouyas   +2 more
doaj   +1 more source