• 대한수학회보
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• 제55권6호
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• pp.1755-1771
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• 2018

In this paper, we investigate a certain type of q-difference Riccati equation in the complex plane. We prove that q-difference Riccati equation possesses a one parameter family of meromorphic solutions if it has three distinct meromorphic solutions. Furthermore, we find that all meromorphic solutions of q-difference Riccati equation and corresponding second order linear q-difference equation can be expressed by q-gamma function if this q-difference Riccati equation admits two distinct rational solutions and $q{\in}{\mathbb{C}}$ such that 0 < ${\mid}q{\mid}$ < 1. The growth and value distribution of differences of meromorphic solutions of q-difference Riccati equation are also treated.

• 대한수학회보
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• 제35권4호
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• pp.653-658
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• 1998

In this paper, we investigate the Hyers-Ulam stability of the (p,k)-MP functional equation.

• 호남수학학술지
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• 제28권2호
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• pp.225-231
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• 2006

We consider an n-dimensional version of the functional equation of $Acz{\acute{e}}l$ and Chung in almost everywhere sense.

• 대한수학회논문집
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• 제14권2호
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• pp.301-310
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• 1999

This paper is concerned with the existence of positive solution of a semilinear elliptic equation with homogeneous Dirichlet boundary condition.

• 충청수학회지
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• 제36권4호
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• pp.231-244
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• 2023

We study the modularity and holomorphic anomaly equation for Hodge-Gromov-Witten invariants of elliptic curves.

• East Asian mathematical journal
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• 제36권1호
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• pp.35-53
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• 2020

In this paper, we investigate Hyers-Ulam-Rassias stability of an additive-quartic functional equation, of a quadratic-quartic functional equation, and of a cubic-quartic functional equation.

• 충청수학회지
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• 제34권3호
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• pp.295-306
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• 2021

The general sextic functional equation is a generalization of many functional equations such as the additive functional equation, the quadratic functional equation, the cubic functional equation, the quartic functional equation and the quintic functional equation. In this paper, motivating the method of Găvruta [J. Math. Anal. Appl., 184 (1994), 431-436], we will investigate the stability of the general sextic functional equation.

• 충청수학회지
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• 제20권2호
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• pp.109-115
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• 2007

In this paper, we obtain the general solution and the stability of the multi-dimensional Cauchy's functional equation $f(x_1+y_1,{\cdots},x_n+y_n)=f(x_1,{\cdots},x_n)+f(y_1,{\cdots},y_n)$. The function f given by $f(x_1,{\cdots},x_n)=a_1x_1+{\cdots}+a_nx_n$ is a solution of the above functional equation.

• 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.

• 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.