Results 11 to 20 of about 1,857 (182)
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
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Hyers–Ulam–Rassias stability of a linear recurrence
Journal of Mathematical Analysis and Applications, 2005 The author considers a linear recurrence \[ x_{n+1}=a_nx_n+b_n,\qquad n\geq 0,\;x_0\in X \] where \((x_n)\) is a sequence in a Banach space \(X\) and \((a_n)\), \((b_n)\) are given sequences of scalars and vectors in \(X\), respectively. Then, a stability result is proved: Suppose that \(\varepsilon>0\), \(| a| >1\) and an arbitrary sequence \((b_n ...
Dorian Popa
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β–Hyers–Ulam–Rassias Stability of Semilinear Nonautonomous Impulsive System [PDF]
Symmetry, 2019 In this paper, we study a system governed by impulsive semilinear nonautonomous differential equations. We present the β –Ulam stability, β –Hyers–Ulam stability and β –Hyers–Ulam–Rassias stability for the said system on a compact interval and then extended it to an unbounded interval. We use Grönwall type inequality and evolution family
Xiaoming Wang, Muhammad Arif, Akbar Zada
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Hyers‐Ulam‐Rassias stability of nonlinear integral equations through the Bielecki metric [PDF]
Mathematical Methods in the Applied Sciences, 2018 We analyse different kinds of stabilities for classes of nonlinear integral equations of Fredholm and Volterra type. Sufficient conditions are obtained in order to guarantee Hyers‐Ulam‐Rassias, σ‐semi‐Hyers‐Ulam and Hyers‐Ulam stabilities for those integral equations. Finite and infinite intervals are considered as integration domains. Those sufficient
Simões, A. M., Castro, L. P.
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The generalized Hyers–Ulam–Rassias stability of a cubic functional equation
Journal of Mathematical Analysis and Applications, 2002 The authors consider the functional equation \[ f(2x+y) +f(2x-y)=2f(x+y)+ 2f(x-y)+12f(x). \] They determine the general solution, which is of the form \(f(x)= B(x,x,x)\) where \(B\) is symmetric and additive in each variable. Moreover they investigate the stability properties of this equation.
Jun, Kil-Woung, Kim, Hark-Mahn
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A Generalization of the Hyers–Ulam–Rassias Stability of Jensen's Equation
Journal of Mathematical Analysis and Applications, 1999 The following generalization of the stability of the Jensen's equation in the spirit of Hyers-Ulam-Rassias is proved: Let \(V\) be a normed space, \(X\) -- a Banach space, \(pa\). For the case \(p>1\) a corresponding result is obtained.
Lee, Yang-Hi, Jun, Kil-Woung
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Hyers–Ulam–Rassias Stability of a Jensen Type Functional Equation
Journal of Mathematical Analysis and Applications, 2000 The author studies the Hyers-Ulam-Rassias stability of a Jensen type functional equation \[ 3f((x+y+z)/3)+ f(x)+ f(y)+ f(z)= 2[ f((x+y)/2)+ f((y+z)/2)+ f((z+x)/2)]. \] The main result of this paper is the following: If the function \(f: X\to Y\) satisfies \[ \begin{multlined}\|3 f((x+y+z)/3)+ f(x)+ f(y)+ f(z)- 2[f((x+y)/2)+ f((y+z)/2)+ f((z+x)/2)]\|\\ \
Tiberiu Trif
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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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Practical Ulam-Hyers-Rassias stability for nonlinear equations [PDF]
Mathematica Bohemica, 2017 In this paper, we offer a new stability concept, practical Ulam-Hyers-Rassias stability, for nonlinear equations in Banach spaces, which consists in a restriction of Ulam-Hyers-Rassias stability to bounded subsets.
Jin Rong Wang, Michal Fečkan
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Hyers–Ulam–Rassias Stability of Hermite’s Differential Equation
Mathematics, 2022 In this paper, we studied the Hyers–Ulam–Rassias stability of Hermite’s differential equation, using Pachpatte’s inequality. We compared our results with those obtained by Blaga et al. Our estimation for zx−yx, where z is an approximate solution and y is an exact solution of Hermite’s equation, was better than that obtained by the authors previously ...
Daniela Marian +2 more
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