• Korean Journal of Mathematics
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• 제16권3호
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• pp.369-378
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• 2008

The aim of this paper is to study the stability problem for the pexider type trigonometric functional equation f(x + y) − f(x−y) = 2g(x)h(y), which is related to the d'Alembert, the Wilson, the sine, and the mixed trigonometric functional equations.

• 호남수학학술지
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• 제30권1호
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• pp.185-195
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• 2008

We consider a system of trigonometric functional equations in the spaces of generalized functions such as Schwartz distributions and Gelfand generalized functions. As a consequence we find locally integrable solutions of the n-dimensional trigonometric functional equation.

• Korean Journal of Mathematics
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• 제29권4호
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• pp.765-774
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• 2021

In this paper, we solve and investigate the superstability of the p-radical functional equations $$f(\sqrt[p]{x^p+y^p})-f(\sqrt[p]{x^p-y^p})={\lambda}f(x)g(y),\\f(\sqrt[p]{x^p+y^p})-f(\sqrt[p]{x^p-y^p})={\lambda}g(x)f(y),$$ which is related to the trigonometric(Kim's type) functional equations, where p is an odd positive integer and f is a complex valued function. Furthermore, the results are extended to Banach algebras.

• 대한수학회논문집
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• 제23권4호
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• pp.567-575
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• 2008

In this article we prove the Hyers.Ulam stability of trigonometric functional equations.

• 한국수학교육학회지시리즈B:순수및응용수학
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• 제18권3호
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• pp.231-244
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• 2011

We prove the Hyers-Ulam stability for trigonometric type functional inequalities in restricted domains with time variables. As consequences of the result we obtain asymptotic behaviors of the inequalities and stability of related functional inequalities in almost everywhere sense.

• 한국해양공학회지
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• 제18권1호
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• pp.7-9
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• 2004

Using the solution to th contour integral of the complex logarithmic function ${\oint}_cIn(z-z_{0})dz$, the following definite integral, derived from the formula to calculate the forces exerted to n circular cylinder by the discrete vortices shed from it, has been evaluated (equation omitted)

• 한국수학교육학회지시리즈B:순수및응용수학
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• 제17권4호
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• pp.397-411
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• 2010

In this paper, we will investigate the superstability for the sine functional equation from the following Pexider type functional equation: $f(x+y)-g(x-y)={\lambda}{\cdot}h(x)k(y)$ ${\lambda}$: constant, which can be considered an exponential type functional equation, the mixed functional equation of the trigonometric function, the mixed functional equation of the hyperbolic function, and the Jensen type equation.

• Journal of Mechanical Science and Technology
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• 제19권spc1호
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• pp.481-486
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• 2005

This paper introduces a numerical method for integration of the linear and nonlinear differential dynamic equation of motion. The variation of acceleration in two time steps is approximated as a combination of both trigonometric cosine and hyperbolic cosine functions with weighted coefficient. From which all necessary formulae are elaborated for the direct integration of the governing equation. A number of linear and nonlinear dynamic problems with various degrees of freedom are analysed using both the suggested method and Newmark method for the comparison. The numerical results show high advantages and effectiveness of the new method.

• Nonlinear Functional Analysis and Applications
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• 제28권3호
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• pp.801-812
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• 2023

In this paper, we investigate the superstability for the p-power-radical sine functional equation $$f\(\sqrt[p]{\frac{x^p+y^p}{2}}\)^2-f\(\sqrt[p]{\frac{x^p-y^p}{2}}\)^2=f(x)f(y)$$ from an approximation of the p-power-radical functional equation: $$f(\sqrt[p]{x^p+y^p})-f(\sqrt[p]{x^p-y^p})={\lambda}g(x)h(y),$$ where p is an odd positive integer and f, g, h are complex valued functions. Furthermore, the obtained results are extended to Banach algebras.

• 대한수학회논문집
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• 제26권4호
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• pp.603-610
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• 2011

In this paper, we propose an algorithm for identifying ${\omega}_j{\in}(0,\;{\infty}),\;a_j,b_j{\in}\mathbb{C}$ and N of the following trigonometric series $f(t)=a_0+ \sum\limits_{j=1}^N[a_jcos{\omega}_jt+b_j\;sin{\omega}_jt]$ by means of the finite number of sample values. We prove that the frequency components are shown to be the solutions of some characteristic equation related to the inverse of a Hankel matrix derived from the sample values.