Results 1 to 10 of about 814 (188)
Hyers‐Ulam‐Rassias stability of generalized derivations [PDF]
International Journal of Mathematics and Mathematical Sciences, 2006 The generalized Hyers‐Ulam‐Rassias stability of generalized derivations on unital Banach algebras into Banach bimodules is established.
Mohammad Sal Moslehian
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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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On the Hyers–Ulam–Rassias Stability of a Quadratic Functional Equation
Journal of Mathematical Analysis and Applications, 1999 The author examines the Hyers-Ulam-Rassias stability [see \textit{D. H. Hyers, G. Isac} and \textit{Th. M. Rassias}, Stability of functional equations in several variables, Birkhäuser, Boston (1998; Zbl 0907.39025)] of the quadratic functional equation \[ f(x-y-z)+f(x)+f(y)+f(z) = f(x-y)+f(y+z)+f(z-x) \] and proves that if a mapping \(f\) from a normed
Soon-Mo Jung
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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, Kil-Woung Jun
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On the Hyers-Ulam-Rassias stability of a pexiderized quadratic inequality [PDF]
Mathematical Inequalities & Applications, 2001 The authors examine the Hyers-Ulam-Rassias stability [see \textit{D. H. Hyers, G. Isac} and \textit{Th. M. Rassias}, Stability of Functional Equations in Several Variables, Birkhäuser, Boston (1998; Zbl 0907.39025); and \textit{Soon-Mo Jung}, Hyers-Ulam-Rassias stability of functional equations in Mathematical Analysis, Hadronic Press, Palm Harbor ...
Kil-Woung Jun, Yang-Hi Lee
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Stability analysis for a class of implicit fractional differential equations involving Atangana–Baleanu fractional derivative [PDF]
Advances in Difference Equations, 2021 Some fundamental conditions and hypotheses are established to ensure the existence, uniqueness, and stability to a class of implicit boundary value problems (BVPs) with Atangana–Baleanu–Caputo type derivative and integral.
Asma +3 more
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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 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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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. Găvruţă
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Hyers-Ulam-Rassias and Ulam-Gavruta-Rassias Stabilities of an Additive Functional Equation in Several Variables [PDF]
International Journal of Mathematics and Mathematical Sciences, 2007 It is well known that the concept of Hyers-Ulam-Rassias stability was originated by Th. M. Rassias (1978) and the concept of Ulam-Gavruta-Rassias stability was originated by J. M. Rassias (1982–1989) and by P. Găvruta (1999).
Paisan Nakmahachalasint
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