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On the Hyers-Ulam Stability of Linear Mappings
Journal of Mathematical Analysis and Applications, 1993 Let \(H\) be a monotonically increasing symmetric homogeneous function of degree \(p\), where \(p\in (0,\infty)\backslash\{1\}\). Let \(f\) be a mapping from a real normed space \(X\) into a real Banach space \(Y\). Assume that \[ \| f(x+ y)- f(x)- f(y)\|\leq H(\| x\| \| y\|)\quad \forall x,\;y\in X. \] The authors proved that \[ T(x)=\lim_{n\to\infty}
Rassias, T.M., Semrl, P.
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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 +2 more
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Hyers–Ulam stability of Euler’s equation
Applied Mathematics Letters, 2011 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Cimpean, Dalia Sabina, Popa, Dorian
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Hyers–Ulam stability of derivations and linear functions [PDF]
Aequationes mathematicae, 2010 9 pages; published in Aequationes Mathematicae in ...
Boros, Zoltán, Gselmann, Eszter
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AIMS Mathematics, 2021 In this manuscript, a class of implicit impulsive Langevin equation with Hilfer fractional derivatives is considered. Using the techniques of nonlinear functional analysis, we establish appropriate conditions and results to discuss existence, uniqueness,
Xiaoming Wang +4 more
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Asymptotic stability of the Cauchy and Jensen functional equations [PDF]
, 2016 The aim of this note is to investigate the asymptotic stability behaviour of the Cauchy and Jensen functional equations. Our main results show that if these equations hold for large arguments with small error, then they are also valid everywhere with a ...
A. Bahyrycz +19 more
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On a general Hyers‐Ulam stability result
International Journal of Mathematics and Mathematical Sciences, 1995 In this paper, we prove two general theorems about Hyers‐Ulam stability of functional equations. As particular cases we obtain many of the results published in the last ten years on the stability of the Cauchy and quadratic equation.
Costanz Borelli, Gian Luigi Forti
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Advances in Difference Equations, 2020 Some essential conditions for existence theory and stability analysis to a class of boundary value problems of fractional delay differential equations involving Atangana–Baleanu-Caputo derivative are established. The deserted results are derived by using
Gauhar Ali +5 more
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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 and Hyers-Ulam-Rassias Stability for a Class of Integro-Differential Equations [PDF]
, 2018 We analyse different kinds of stabilities for a class of very general nonlinear integro-differential equations of Volterra type within appropriate metric spaces. Sufficient conditions are obtained in view to guarantee Hyers-Ulam stability and Hyers-Ulam-Rassias stability for such a class of integro-differential equations. We will consider the different
Castro, L. P., Simões, A. M.
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