• Kyungpook Mathematical Journal
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• v.51 no.3
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• pp.251-260
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• 2011

The aim of this paper is to obtain a solution of a certain multidimensional convolution integral equation of Fredholm type whose kernel involves a generalized polynomial set. A number of results follow as special cases from the main theorem by specifying the parameters of the generalized polynomial set.

• Honam Mathematical Journal
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• v.40 no.1
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• pp.139-153
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• 2018

Let $P{\geq}3$ be an integer and let ($U_n$) denote generalized Fibonacci sequence defined by $U_0=0$, $U_1=1$ and $U_{n+1}=PU_n-U_{n-1}$ for $n{\geq}1$. In this study, when P is odd, we solve the equation $U_n=11x^2+1$. We show that only $U_1$ and $U_2$ may be of the form $11x^2+1$.

• The Transactions of the Korean Institute of Electrical Engineers
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• v.33 no.12
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• pp.491-496
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• 1984

The optimal control and filtering problems for the systems with the generalized state space model are considered and the generalized Riccati equation is derived. Also the algorithm for the solution of the generalized algebraic Riccati equation is developed and it is shown that the algotithm can be applied to the case where the matrix R is singular or near singular.

• Communications of the Korean Mathematical Society
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• v.36 no.2
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• pp.299-312
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• 2021

The main aim of this paper is to introduce and study the generalized Laguerre polynomials and prove that these polynomials are characterized by the generalized hypergeometric function. Also we investigate some properties and formulas for these polynomials such as explicit representations, generating functions, recurrence relations, differential equation, Rodrigues formula, and orthogonality.

• Honam Mathematical Journal
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• v.31 no.3
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• pp.451-462
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• 2009

In this paper we prove the superstability of a generalized exponential functional equation $f(x+y)=a^{2xy-1}g(x)f(y)$. It is a generalization of the superstability theorem for the exponential functional equation proved by Baker. Also we investigate the stability of this functional equation in the following form : ${\frac{1}{1+{\delta}}}{\leq}{\frac{f(x+y)}{a^{2xy-1}g(x)f(y)}}{\leq}1+{\delta}$.

• Bulletin of the Korean Mathematical Society
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• v.42 no.1
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• pp.57-73
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• 2005

In this paper we solve a generalized quadratic Jensen type functional equation $m^2 f (\frac{x+y+z}{m}) + f(x) + f(y) + f(z) =n^2 [f(\frac{x+y}{n}) +f(\frac{y+z}{n}) +f(\frac{z+x}{n})]$ and prove the stability of this equation in the spirit of Hyers, Ulam, Rassias, and Gavruta.

• The Pure and Applied Mathematics
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• v.26 no.2
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• pp.85-97
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• 2019

In this paper we introduce the reciprocal-negative Fermat's equation induced by the famous equation in the Fermat's Last Theorem, establish the general solution in the simplest cases and the differential solution to the equation, and investigate, then, the generalized Hyers-Ulam stability in a $quasi-{\beta}-normed$ space with both the direct estimation method and the fixed point approach.

• Journal of the Chungcheong Mathematical Society
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• v.26 no.4
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• pp.887-900
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• 2013

In this paper, we investigate the stability for the functional equation f(3x+y)-3f(2x+y)+3f(x+y)-f(y)=0 in the sense of M. S. Moslehian and Th. M. Rassias.

• Journal of the Chungcheong Mathematical Society
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• v.31 no.2
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• pp.199-230
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• 2018

In this paper, we introduce the general form of a viginti functional equation. Then, we find the general solution and study the generalized Ulam-Hyers stability of such functional equation in multi-Banach spaces by using fixed point technique. Also, we indicate an example for non-stability case regarding to this new functional equation.

• Bulletin of the Korean Mathematical Society
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• v.38 no.2
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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.