• 대한수학회보
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• 제58권2호
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• pp.269-275
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• 2021

Let ℝ be the set of real numbers, f, g : ℝ → ℝ and �� ≥ 0. In this paper, we consider the stability of partially pexiderized exponential-radical functional equation $$f({\sqrt[n]{x^N+y^N}})=f(x)g(y)$$ for all x, y ∈ ℝ, i.e., we investigate the functional inequality $$\|f({\sqrt[n]{x^N+y^N}})-f(x)g(y)\|{\leq}{\epsilon}$$ for all x, y ∈ ℝ.

• 전기학회논문지
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• 제59권2호
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• pp.423-428
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• 2010

In the initial design phase of superscalar microprocessors, a performance model is necessary. A theoretic performance model is very useful since performance for various architecture parameters can be obtained by simply computing equations, without repeating simulations, Previous studies established theoretic performance models using the relation between the instruction window size and the issue width, with the penalties due to branch mispredictions and cache misses. However, the study was intended for unlimited number of functional units, which is insufficient for the real case application. This paper proposes a superscalar microprocessor theoretical performance model which also works for the limited functional units. To enhance the accuracy of our limited functional unit model, instruction dependency rates are employed. By using trace-driven data of SPEC 2000 integer programs as input, this paper shows that the theoretically computed performance of superscalar microprocessor with limited number of functional units is quite similar to the measured performance.

• 한국수학교육학회지시리즈B:순수및응용수학
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• 제14권1호
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• pp.7-14
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• 2007

The aim of this paper is to study the superstability problem of the cosine type functional equation f(x+y)+f(x+${\sigma}y$)=2g(x)g(y).

• East Asian mathematical journal
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• 제35권3호
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• pp.351-356
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• 2019

In this paper, we investigate Hyers-Ulam-Rassias stability of the general quartic functional equation f(5x + y) - 5f(4x + y) + 10f(3x + y) - 10f(2x + y) + 5f(x + y) - f(y) = 0.

• 호남수학학술지
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• 제46권1호
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• pp.146-167
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• 2024

In this paper, we investigate the stability of the general decic functional equation $$\sum_{i=0}^{11}_{11}C_i(-1)^{11-i}f(x+iy)=0$$ in the sense of Rassias.

• 호남수학학술지
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• 제27권1호
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• pp.51-68
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• 2005

In this paper we solve a generalized Popoviciu functional equation and investigate the stability of this equation.

• 대한수학회지
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• 제38권2호
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• pp.437-468
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• 2001

This paper is an exposition of the relationship between Witten's functional integral and Vassiliev invariants.

• 대한수학회논문집
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• 제31권4호
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• pp.819-825
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• 2016

In this paper, we establish approximation of bi-quadratic functional equations in Lipschitz spaces.

• 대한전자공학회:학술대회논문집
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• 대한전자공학회 2003년도 신호처리소사이어티 추계학술대회 논문집
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• pp.489-492
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• 2003

In this paper, we propose an iterative mixed norm image restoration algorithm using multi regularization parameters. A functional which combines the regularized l$_2$ norm functional and the regularized l$_4$ functional is proposed. The smoothness of each functional is determined by the regularization parameters. Also, a regularization parameter is used to determine the relative importance between the regularized l$_2$ functional and the regularized l$_4$ functional. An iterative algorithm is utilized for obtaining a solution and its convergence is analyzed.

• Journal of applied mathematics & informatics
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• 제14권1_2호
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• pp.415-422
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• 2004

In this paper, we investigate the Hyers-Ulam stability and the super-stability of the functional equation f(x＋y＋rxy) = f(x)＋f(y)＋rxf(y)＋ryf(x) which is obtained by combining the additive Cauchy functional equation and the derivation functional equation.