• Title/Summary/Keyword: quadratic equation

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ON STABILITY OF A QUADRATIC FUNCTIONAL EQUATION

  • Jun, Kil-Woung;Kim, Hark-Mann;Lee, Don O
    • Journal of the Chungcheong Mathematical Society
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    • v.15 no.2
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    • pp.73-84
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    • 2003
  • In this paper, we investigate the new quadratic type functional equation f(2x + y) - f(x + 2y) = 3f(x) - 3f(y) and prove the stablility of this equation in the spirit of Hyers, Ulam, Rassias and G$\breve{a}$vruţa.

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ON THE ULAM STABILITY PROBLEM OF A QUADRATIC FUNCTIONAL EQUATION

  • Bae, Jae-Hyeong;Chang, Ick-Soon
    • Journal of applied mathematics & informatics
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    • v.8 no.2
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    • pp.561-567
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    • 2001
  • In this paper, we investigate the Hyers-Ulam-Rassias stability of a quadratic functional equation f(x+y+z)+f(x-y)+f(y-z)+f(x-z) = 3f(x)+3f(y)+3f(z) and prove the Hyers-Ulam stability of the equation on bounded domains.

THE CONDITION NUMBERS OF A QUADRATIC MATRIX EQUATION

  • Kim, Hye-Yeon;Kim, Hyun-Min
    • East Asian mathematical journal
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    • v.29 no.3
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    • pp.327-335
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    • 2013
  • In this paper we consider the quadratic matrix equation which can be defined by $$Q(X)=AX^2+BX+C=0$$, where X is a $n{\times}n$ unknown complex matrix, and A, B and C are $n{\times}n$ given matrices with complex elements. We first introduce a couple of condition numbers of the equation Q(X) and present normwise condition numbers. Finally, we compare the results and some numerical experiments are given.

STABILITY OF AN n-DIMENSIONAL QUADRATIC FUNCTIONAL EQUATION

  • Jin, Sun-Sook;Lee, Yang-Hi
    • Journal of the Chungcheong Mathematical Society
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    • v.31 no.4
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    • pp.397-409
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    • 2018
  • In this paper, we investigate the generalized Hyers-Ulam stability of the functional equation $$f\({\sum\limits_{i=1}^{n}}x_i\)+{\sum\limits_{1{\leq}i<j{\leq}n}}f(x_i-x_j)-n{\sum\limits_{i=1}^{n}f(x_i)=0$$ for integer values of n such that $n{\geq}2$, where f is a mapping from a vector space V to a Banach space Y.

A Fixed Point Approach to the Stability of Quadratic Equations in Quasi Normed Spaces

  • Mirmostafaee, Alireza Kamel
    • Kyungpook Mathematical Journal
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    • v.49 no.4
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    • pp.691-700
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    • 2009
  • We use the fixed alternative theorem to establish Hyers-Ulam-Rassias stability of the quadratic functional equation where functions map a linear space into a complete quasi p-normed space. Moreover, we will show that the continuity behavior of an approximately quadratic mapping, which is controlled by a suitable continuous function, implies the continuity of a unique quadratic function, which is a good approximation to the mapping. We also give a few applications of our results in some special cases.