منابع مشابه
Orthogonal stability of mixed type additive and cubic functional equations
In this paper, we consider orthogonal stability of mixed type additive and cubic functional equation of the form $$f(2x+y)+f(2x-y)-f(4x)=2f (x+y)+2f(x-y)-8f(2x) +10f(x)-2f(-x),$$ with $xbot y$, where $bot$ is orthogonality in the sense of Ratz.
متن کاملorthogonal stability of mixed type additive and cubic functional equations
in this paper, we consider orthogonal stability of mixed type additive and cubic functional equation of the form $$f(2x+y)+f(2x-y)-f(4x)=2f (x+y)+2f(x-y)-8f(2x) +10f(x)-2f(-x),$$ with $xbot y$, where $bot$ is orthogonality in the sense of ratz.
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We obtain an essentially optimal estimate for the moment of order 32/3 of the exponential sum having argument αx + βx. Subject to modest local solubility hypotheses, we thereby establish that pairs of diagonal Diophantine equations, one cubic and one quadratic, possess nontrivial integral solutions whenever the number of variables exceeds 10.
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We investigate the number of integral solutions possessed by a pair of diagonal cubic equations in a large box. Provided that the number of variables in the system is at least thirteen, and in addition the number of variables in any non-trivial linear combination of the underlying forms is at least seven, we obtain a lower bound for the order of magnitude of the number of integral solutions con...
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* Correspondence: abasalt. [email protected] Department of Mathematics, Garmsar Branch, Islamic Azad University, Garmsar, Iran Full list of author information is available at the end of the article Abstract In this paper, we prove the Hyers-Ulam stability and the superstability for cubic functional equation by using the fixed point alternative theorem. As a consequence, we show that the cubic m...
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ژورنال
عنوان ژورنال: Proceedings of the London Mathematical Society
سال: 1977
ISSN: 0024-6115
DOI: 10.1112/plms/s3-34.2.354