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A HYPERSTABILITY RESULT FOR THE CAUCHY EQUATION
AbstractWe prove a hyperstability result for the Cauchy functional equation$f(x+ y)= f(x)+ f(y)$, which complements some earlier stability outcomes of J. M. Rassias. As a consequence, we obtain the slightly surprising corollary that for every function$f$, mapping a normed space${E}_{1} $into a normed space${E}_{2} $, and for all real numbers$r, s$with ...
Brzdek, J.
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On the hyperstability of time-varying blocks
IEEE Transactions on Automatic Control, 1970The hyperstability of linear time-varying discrete blocks is studied. Sufficient conditions for hyperstability are obtained for special classes of multiple and simple blocks.
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Hyperstability of the Jensen functional equation
Acta Mathematica Hungarica, 2013\textit{S.-M. Jung}, \textit{M. S. Moslehian} and \textit{P. K. Sahoo} [J. Math. Inequal. 4, No. 2, 191--206 (2010; Zbl 1219.39016)] investigated the conditional stability of the generalized Jensen functional equation \(f(ax+by)=af(x)+bf(y)\). Based on a fixed point method, the authors of the present paper consider the hyperstability problem of the ...
Magdalena Piszczek, Anna Bahyrycz
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On hyperstability of the biadditive functional equation
Acta Mathematica Scientia, 2017Abstract We present results on approximate solutions to the biadditive equation f ( x + y , z - w ) + f ( x - y , z + w ) = 2 f ( x , z ) - 2 f ( y , w ) on a restricted domain. The proof is based on a quite recent fixed point theorem in some function spaces.
Iz-Iddine El-Fassi +2 more
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