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A New Approach to the Hyers–Ulam–Rassias Stability of Differential Equations
Results in Mathematics, 2021zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Choubin, Mehdi, Javanshiri, Hossein
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Hyers-Ulam-Rassias Stability of a Cubic Functional Equation [PDF]
Bulletin of the Korean Mathematical Society, 2007 In this paper, we will find out the general solution and investigate the generalized Hyers-Ulam-Rassias stability problem for the following cubic functional equation 3f(x+3y)+f(3x-y)=15f(x+y)+15f(x-y)+80f(y). The concept of Hyers-Ulam-Rassias stability originated from Th. M. Rassias# stability theorem that appeared in his paper: On the stability of the
Abbas Najati
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HYERS–ULAM–RASSIAS STABILITY FOR NONAUTONOMOUS DYNAMICS
Rocky Mountain Journal of MathematicsThe authors study semilinear equations \begin{align*} x'&=A(t)x+f(t,x),\\ x_{n+1}&=A_nx_n+f_n(x_n) \end{align*} on the nonnegative half-line in a Banach space \(X\). Provided the linear part is uniformly exponentially stable, Hyers-Ulam-Rassias stability is established, if the (uniform) Lipschitz constant of the nonlinearity is small.
Dragičević, Davor +1 more
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Hyers–Ulam–Rassias Stability on Amenable Groups
2016In this chapter, we study the Ulam–Hyers–Rassias stability of the generalized cosine-sine functional equation: $$\displaystyle{\int _{K}\int _{G}f(xtk \cdot y)d\mu (t)dk = f(x)g(\,y) + h(\,y),\;x,y \in G,}$$ where f, g, and h are continuous complex valued functions on a locally compact group G, K is a compact subgroup of morphisms of G, dk is ...
Mohamed Akkouchi +2 more
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On the Hyers-Ulam-Rassias Stability of Mappings
1998We give an answer to a question of Hyers and Rassias [5] concerning the stability of mappings.
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On Hyers-Ulam-Rassias stability of functional equations
Acta Mathematica Sinica, English Series, 2008Let \(G_1\) and \(G_2\) be two groups. We say that \(f, g, h, p, q :G_1\to G_2\) are the pseudo-additive mappings of the mixed quadratic and Pexider type in \(G_1\) if \[ f(x+y+z)+g(x+y)-h(x)-p(y)-q(z)=0 \] for all \(x, y, z \in G_1.\) In this paper the author investigates the Hyers-Ulam-Rassias stability of the functional equation above.
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Hyers–Ulam–Rassias Stability of Derivations in Proper JCQ*–triples
Mediterranean Journal of Mathematics, 2013zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Eskandani, Golamreza Zamani +1 more
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Hyers-Ulam-Rassias Stability for a Multivalued Iterative Equation
Acta Mathematica Scientia, 2008Abstract Because multifunctions do not have so good properties as single-valued functions, only the existence of solutions of the polynomial-like iterative equation of order 2 is discussed for multifunctions. This article gives conditions for its Hyers-Ulam-Rassias stability.
Zhang Wanxiong, Xu Bing
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On the Hyers-Ulam-Rassias Stability of a Functional Equation
2003In this paper, we will introduce a new functional equation f (x 1, y 1) f (x 2, y 2) = f (x 1 x 2+ y 1 y 2, x 1 y 2 − y 1 x 2), which is strongly related to a well known elementary formula of number theory, and investigate the solutions of the equation. Moreover, we will also study the Hyers—Ulam—Rassias stability of that equation.
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A new method for the generalized Hyers-Ulam-Rassias stability
2010We propose a new method, called the textit{the weighted space method}, for the study of the generalized Hyers-Ulam-Rassias stability. We use this method for a nonlinear functional equation, for Volterra and Fredholm integral operators.
Gavruta, P., Gavruta, L.
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