• Journal of the Korean Society for Industrial and Applied Mathematics
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• 제27권1호
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• pp.23-36
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• 2023

The vector wave equation is widely used in electromagnetic wave analysis. This paper solves the vector wave equation using curl-conforming finite elements. The variational problem is established from Riesz functional based on vector wave equation and the unique existence of weak solution is explored. The edge elements are used in computation and the simulation results are compared with those obtained from a commercial simulator, ANSYS HFSS (high-frequency structure simulator).

• Journal of applied mathematics & informatics
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• 제15권1_2호
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• pp.435-446
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• 2004

In this paper, we obtain the general solution of a quadratic functional equation $b^2f(\frac{x+y+z}{b})+f(x-y)+f(x-z)=\;a^2[f(\frac{x-y-z}{a})+f(\frac{x+y}{a})+f(\frac{x+z}{a})]$ and prove the stability of this equation.

• Korean Journal of Mathematics
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• 제26권4호
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• pp.615-628
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• 2018

In this paper, we introduce the pioneering trigintic functional equation. Moreover, we establish the general solution of the trigintic functional equation and prove the Hyers-Ulam sum and product stabilities of the same equation in multi-Banach spaces by employing the fixed point approach.

• 대한수학회보
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• 제39권2호
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• pp.225-236
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• 2002

By means of the method of majorant series, sufficient conditions are obtained for the existence of analytic solutions of a functional differential equation with proportional delays.

• 대한수학회보
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• 제36권2호
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• pp.287-303
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• 1999

The general solution of the functional equation f1(pr, qs) + f2(ps, qr) = g(p,q) + h(r,s) for p, q, r, s $\in$] 0, 1[will be investigated without any regularity assumptions on the unknown functions f1, f2, g, h:]0.1[->R.

• 한국수학교육학회지시리즈B:순수및응용수학
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• 제13권4호
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• pp.295-301
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• 2006

We Investigate the relation between the multi-variable bi-additive functional equation f(x+y+z,u+v+w)=f(x,u)+f(x,v)+f(x,w)+f(y,u)+f(y,v)+f(y,w)+f(z,u)+f(z,v)+f(z,w) and the multi-variable quadratic functional equation g(x+y+z)+g(x-y+z)+g(x+y-z)+g(-x+y+z)=4g(x)+4g(y)+4g(z). Furthermore, we find out the general solution of the above two functional equations.

• 대한수학회논문집
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• 제23권2호
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• pp.191-199
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• 2008

We investigate the relation between the vector variable bi-additive functional equation $f(\sum\limits^n_{i=1} xi,\;\sum\limits^n_{i=1} yj)={\sum\limits^n_{i=1}\sum\limits^n_ {j=1}f(x_i,y_j)$ and the multi-variable quadratic functional equation $$g(\sum\limits^n_{i=1}xi)\;+\;\sum\limits_{1{\leq}i<j{\leq}n}\;g(x_i-x_j)=n\sum\limits^n_{i=1}\;g(x_i)$$. Furthermore, we find out the general solution of the above two functional equations.

• Kyungpook Mathematical Journal
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• 제50권4호
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• pp.557-564
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• 2010

By using an idea of C$\u{a}$dariu and Radu [4], we prove the generalized Hyers-Ulam stability of the functional equation f(x + y,z - w) + f(x - y,z + w) = 2f(x, z) + 2f(y, w). The quadratic form $f\;:\;\mathbb{R}\;{\times}\;\mathbb{R}{\rightarrow}\mathbb{R}$ given by f(x, y) = $ax^2\;+\;by^2$ is a solution of the above functional equation.

• 한국수학교육학회지시리즈B:순수및응용수학
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• 제29권2호
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• pp.189-199
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• 2022

In this paper, we introduce a new generalized (a, b)-cubic Euler-Lagrange-Jensen functional equation and obtain its general solution. Furthermore, we prove the Hyers-Ulam stability of the new generalized (a, b)-cubic Euler-Lagrange-Jensen functional equation in orthogonality normed spaces.

• 대한수학회보
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• 제52권6호
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• pp.1759-1776
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• 2015

We determine the general solution of the generalized additive-quartic functional equation f(x + 3y) + f(x - 3y) + f(x + 2y) + f(x - 2y) + 22f(x) - 13 [f(x + y) + f(x - y)] + 24f(y) - 12f(2y) = 0 without assuming any regularity conditions on the unknown function f : ${\mathbb{R}}{\rightarrow}{\mathbb{R}}$ and its stability is investigated.