• 충청수학회지
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• 제33권1호
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• pp.9-18
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• 2020

In this paper, we investigate the stability of a quadratic-cubic-quartic functional equation $$f(x+ky)+f(x-ky)-k^2f(x+y)-k^2f(x-y)-2(1-k^2)f(x)-{\frac{k^2(k^2-1)}{6}}(f(2y)+2f(-y)-6f(y))=0$$ by applying the direct method in the sense of Gǎvruta.

• 충청수학회지
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• 제15권2호
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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.

• Journal of applied mathematics & informatics
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• 제8권2호
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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.

• Korean Journal of Mathematics
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• 제28권2호
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• pp.159-168
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• 2020

In this paper, we investigate Hyers-Ulam-Rassias stability of a functional equation f(x + ky) + f(x - ky) - k²f(x + y) - k²f(x - y) + 2(k² - 1)f(x) + (k² + k³)f(y) + (k² - k³)f(-y) - 2f(ky) = 0.

• 대한수학회보
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• 제38권2호
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• pp.325-336
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• 2001

In this paper, we investigate the generalized Hyers-Ulam-Rassias stability of a quadratic function equation f(x+y+z)+f(x-y)+f(y-z)+f(z-x)=3f(x)+3f(y)+3f(z) and prove the Hyers-Ulam-Rassias stability of the equation on bounded domain.

• East Asian mathematical journal
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• 제29권3호
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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.

• 호남수학학술지
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• 제41권4호
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• pp.813-821
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• 2019

In this paper, we investigate Hyers-Ulam-Rassias stability of a functional equation f(x + ky) + f(x - ky) - k²f(x + y) - k²f(x - y) + 2(k² - 1)f(x) + (k² + k)f(y) + (k² - k)f(-y) - 2f(ky) = 0.

• 충청수학회지
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• 제31권4호
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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.

• 충청수학회지
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• 제32권3호
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• pp.295-307
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• 2019

In this paper, we investigate Hyers-Ulam-Rassias stability of the functional equation $$f(x+ky)-{\frac{k^2+k}{2}}f(x+y)+(k^2-1)f(x)-{\frac{k^2-k}{2}}f(x-y)\\{\hfill{67}}-f(ky)+{\frac{k^2+k}{2}}f(y)+{\frac{k^2-k}{2}}f(-y)=0.$$

• Kyungpook Mathematical Journal
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• 제49권4호
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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.