Results 21 to 30 of about 6,753 (236)
On Hyers-Ulam-Rassias stability of a quadratic functional equation [PDF]
Mathematical Inequalities & Applications, 2003 The authors investigate the stability of the `quadratic' functional equation \[ \begin{multlined} f(x+y+z+w)+ 2f(x)+2f(y) +2f(z)+2f(w)\\ =f(x+y)+ f(y+z)+f(z+x) +f(x+w)+ f(y+w)+f(z+w).\end{multlined} \] {}.
Ick-Soon Chang +2 more
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A Generalization of the Hyers-Ulam-Rassias Stability of Approximately Additive Mappings
Journal of Mathematical Analysis and Applications, 1994 The author proves a generalization of the stability of approximately additive mappings in the spirit of Hyers, Ulam and Rassias.
P. Gǎvruţa
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HYERS-ULAM-RASSIAS STABILITY OF A QUADRATIC TYPE FUNCTIONAL EQUATION [PDF]
Bulletin of the Korean Mathematical Society, 2003 The authors prove that if a function \(f\), from a real vector space \(X\) into a real vector space \(Y\), satisfies the function equation \[ \begin{multlined} Df(x,y,z):= a^2 f\Biggl({x+ y+ z\over a}\Biggr)+ a^2 f\Biggl({x- y+z\over a}\Biggr)+ a^2 f\Biggl({x+ y-z\over a}\Biggr)\\ +a^2 f\Biggl({-x+ y+z\over a}\Biggr)- 4f(x)- 4f(y)- 4f(z)= 0\end ...
Sang-Han Lee, Kil-Woung Jun
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Hyers-Ulam-Rassias stability of Jensen's equation and its application [PDF]
Proceedings of the American Mathematical Society, 1998 The Hyers-Ulam-Rassias stability for the Jensen functional equation is investigated, and the result is applied to the study of an asymptotic behavior of the additive mappings; more precisely, the following asymptotic property shall be proved: Let X X and Y Y be a real normed space and a real Banach space ...
Soon-Mo Jung
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Hyers‐Ulam‐Rassias‐Wright Stability for Fractional Oscillation Equation [PDF]
Discrete Dynamics in Nature and Society, 2022 In this paper, we consider the nonhomogeneous fractional delay oscillation equation with order σ and introduce a class of control functions, i.e., Wright functions. Next, we apply the Cădariu‐Radu method to prove the existence of a unique solution and Hyers‐Ulam‐Rassias‐Wright stability of the fractional delay oscillation equation.
Zahra Eidinejad, Reza Saadati
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A Generalization of the Hyers–Ulam–Rassias Stability of the Pexider Equation
Journal of Mathematical Analysis and Applications, 2000 Let \(V\) be a normed vector space and \(X\) a Banach space, and let \(f,g,h: V\to X\). The authors prove that the Pexider equation \[ f(x+y)= g(x)+h(y) \] is stable in the following sense: If there exists a real number \(p\neq 1\), such that \[ \bigl\|f(x+y)- g(x)-h(y) \bigr\|\leq\|x \|^p+ \|y\|^p \] for all \(x,y\in V\setminus \{0\}\), then there ...
Yang-Hi Lee, K. Jun
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On the stability of first order impulsive evolution equations [PDF]
Opuscula Mathematica, 2014 In this paper, concepts of Ulam-Hyers stability, generalized Ulam-Hyers stability, Ulam-Hyers-Rassias stability and generalized Ulam-Hyers-Rassias stability for impulsive evolution equations are raised.
JinRong Wang, Michal Fečkan, Yong Zhou
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Hyers-Ulam-Rassias stability of a generalized Pexider functional equation [PDF]
Banach Journal of Mathematical Analysis, 2007 In this interesting paper, the authors investigate the generalized Hyers-Ulam stability for a functional equation of Pexider type on groups.
A. Charifi +2 more
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Aboodh transform and the stability of second order linear differential equations
Advances in Difference Equations, 2021 In this paper, we introduce a new integral transform, namely Aboodh transform, and we apply the transform to investigate the Hyers–Ulam stability, Hyers–Ulam–Rassias stability, Mittag-Leffler–Hyers–Ulam stability, and Mittag-Leffler–Hyers–Ulam–Rassias ...
Ramdoss Murali +3 more
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Hyers-Ulam-Rassias Stability for Linear and Semi-Linear Systems of Differential Equations [PDF]
مجلة جامعة النجاح للأبحاث العلوم الطبيعية, 2018 This paper considers Hyers-Ulam-Rassias Stability for Linear and Semi-Linear Systems of Differential Equations. We establish sufficient conditions of Hyers-Ulam-Rassias stability and Hyers-Ulam stability for linear and semi-linear systems of differential
Maher Qarawani
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