• 한국수학교육학회지시리즈B:순수및응용수학
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• 제11권4호
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• pp.323-335
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• 2004

In this paper, we solve the general solution of a modified additive and quadratic functional equation f(χ + 3y) + 3f(χ-y) = f(χ-3y) + 3f(χ+y) in the class of functions between real vector spaces and obtain the Hyers-Ulam-Rassias stability problem for the equation in the sense of Gavruta.

• 대한수학회논문집
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• 제16권1호
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• pp.103-111
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• 2001

In this paper, we investigate a generalization of the stability of a new quadratic functional equation f(∑(sub)i=1(sup)n x(sub)i)+∑(sub)1$\leq$i$\leq$n f(x(sub)i-x(sub)j) = n∑(sub)i=1(sup)n f(x(sub)i) (n$\geq$2) in the spirits of Hyers, Ulam, Rassias and Gavruta.

• 호남수학학술지
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• 제38권4호
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• pp.693-699
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• 2016

The purpose of this note is to provide an alternative proof of two quadratic transformations contiguous to that of Kummer using a differential equation approach.

• Journal of applied mathematics & informatics
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• 제9권1호
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• pp.415-421
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• 2002

We extend the Hyers-Ulsam-Rassias stability of a quadratic functional equation f(χ+y+z)+f(χ-y)+f(y-Z)+f(χ-z) = 3f(χ)+3f(y)+3f(z) to Banach modules over a Banach algebra.

• 충청수학회지
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• 제20권1호
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• pp.23-29
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• 2007

Let X and Y be vector spaces. In this paper we prove that a mapping $f:X{\rightarrow}Y$ satisfies the following functional equation $${\large}\sum_{1{\leq}k<l{\leq}n}\;(f(x_k+x_l)+f(x_k-x_l))-2(n-1){\large}\sum_{i=1}^{n}f(x_i)=0$$ if and only if the mapping f is quadratic. In addition we investigate the generalized Hyers-Ulam-Rassias stability problem for the functional equation.

• 충청수학회지
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• 제33권1호
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• pp.77-87
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• 2020

In this paper, we investigate the stability of a functional equation f(x + 3y) - 5f(x + 2y) + 10f(x + y) - 8f(x) + 5f(x - y) - f(x - 2y) - 2f(-x) - f(2x) + f(-2x) = 0 by using the fixed point theory in the sense of L. Cǎdariu and V. Radu.

• East Asian mathematical journal
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• 제35권5호
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• pp.559-568
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• 2019

In this paper, we investigate the stability problems for a functional equation f(x + 2y)+f(x - 2y) - 4f(x + y) - 4f(x - y) + 6f(x) - 2f(2y) + 12f(y) - 4f(-y) = 0 by using the fixed point theory in the sense of L. C˘adariu and V. Radu.

• 한국수학교육학회지시리즈B:순수및응용수학
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• 제26권1호
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• pp.49-58
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• 2019

In this paper, I prove the stability problem for a quadratic-cubic functional equation $$f(x+ky)-k^2f(x+y)-k^2f(x-y)+f(x-ky)+f(kx)-{\frac{k^3-3k^2+4}{2}}f(x)+{\frac{k^3-k^2}{2}}f(-x)=0$$ in modular spaces by applying the direct method.

• East Asian mathematical journal
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• 제38권1호
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• pp.95-105
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• 2022

In this paper, we consider a quadratic matrix equation Q(X) = AX² + BX + C = 0 where A, B, C ∈ ℝ^n×n. A new approach is proposed to find solutions of Q(X), using the novel structure of the information processing system. We also present some numerical experimetns with Artificial Neural Network.

• 호남수학학술지
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• 제35권3호
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• pp.417-433
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• 2013

We consider the iterative solution of a quadratic matrix equation with special coefficient matrices which arises in the quasibirth and death problem. In this paper, we show that the elementwise minimal positive solvent of the quadratic matrix equations can be obtained using Newton's method if there exists a positive solvent and the convergence rate of the Newton iteration is quadratic if the Fr$\acute{e}$chet derivative at the elementwise minimal positive solvent is nonsingular. Although the Fr$\acute{e}$chet derivative is singular, the convergence rate is at least linear. Numerical experiments of the convergence rate are given.