• Journal of the Korean Mathematical Society
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• v.41 no.3
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• pp.501-511
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• 2004

We prove the Hyers-Ulam-Rassias stability of the Davison functional equation f($\chi$y) + f($\chi$ + y) = f($\chi$y + $\chi$) + f(y) for a class of functions from a ring into a Banach space and we also investigate the Davison equation of Pexider type.

• Honam Mathematical Journal
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• v.22 no.1
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• pp.37-46
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• 2000

We prove the stability of a generalized Cauchy functional equation of the form ; $$f(a_1x+a_2y)=b_1f(x)+b_2f(y)+w.$$ That is, we obtain a partial answer for the open problem which was posed by the Th.M Rassias and J. Tabor on the stability for a generalized functional equation.

• Honam Mathematical Journal
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• v.30 no.3
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• pp.567-579
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• 2008

We obtain generalized super stability of Cauchy's gamma-beta functional equation B(x, y) f(x + y) = f(x)f(y), where B(x, y) is the beta function and also generalize the stability in the sense of R. Ger of this equation in the following setting: ${\mid}{\frac{B(x,y)f(x+y)}{f(x)f(y)}}-1{\mid}$ < H(x,y), where H(x,y) is a homogeneous function of dgree p(0 ${\leq}$ p < 1).

• Bulletin of the Korean Mathematical Society
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• v.58 no.2
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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.

• Structural Engineering and Mechanics
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• v.85 no.3
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• pp.315-335
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• 2023

Limited studies are available on the mathematical estimates of the compressive strength (CS) of glass fiber-embedded polymer (glass-FRP) compressive elements. The present study has endeavored to estimate the CS of glass-FRP normal strength concrete (NSTC) compression elements (glass-FRP-NSTC) employing two various methodologies; mathematical modeling and artificial neural networks (ANNs). The dataset of 288 glass-FRP-NSTC compression elements was constructed from the various testing investigations available in the literature. Diverse equations for CS of glass-FRP-NSTC compression elements suggested in the previous research studies were evaluated employing the constructed dataset to examine their correctness. A new mathematical equation for the CS of glass-FRP-NSTC compression elements was put forwarded employing the procedures of curve-fitting and general regression in MATLAB. The newly suggested ANN equation was calibrated for various hidden layers and neurons to secure the optimized estimates. The suggested equations reported a good correlation among themselves and presented precise estimates compared with the estimates of the equations available in the literature with R²= 0.769, and R² =0.9702 for the mathematical and ANN equations, respectively. The statistical comparison of diverse factors for the estimates of the projected equations also authenticated their high correctness for apprehending the CS of glass-FRP-NSTC compression elements. A broad parametric examination employing the projected ANN equation was also performed to examine the effect of diverse factors of the glass-FRP-NSTC compression elements.

• Bulletin of the Korean Mathematical Society
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• v.51 no.4
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• pp.1087-1100
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• 2014

We present an accurate and efficient numerical method for solving the Black-Scholes equation. The method uses an adaptive grid technique which is based on a far-field boundary position and the Peclet condition. We present the algorithm for the automatic adaptive grid generation: First, we determine a priori suitable far-field boundary location using the mathematical model parameters. Second, generate the uniform fine grid around the non-smooth point of the payoff and a non-uniform grid in the remaining regions. Numerical tests are presented to demonstrate the accuracy and efficiency of the proposed method. The results show that the computational time is reduced substantially with the accuracy being maintained.

• Journal of the Chungcheong Mathematical Society
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• v.20 no.2
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• pp.163-172
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• 2007

In this paper, we prove the Hyers-Ulam-Rassias stability of a Cauchy-Jensen functional equation $$2f(x+y,\frac{z+w}{2})=f(x,z)+f(x,w)+f(y,z)+f(y,w)$$.

• Journal of the Korean Mathematical Society
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• v.38 no.3
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• pp.645-656
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• 2001

In this paper, we will prove the Hyers-Ulam stability of the quadratic functional equation of Pexider type, f$_1$(x+y) + F$_2$(x-y) = f$_3$(x) + f$_4$(y).

• Honam Mathematical Journal
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• v.32 no.4
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• pp.537-544
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• 2010

We prove the superstability of a functional inequality associated with general exponential functions as follows; ${\mid}f(x+y)-a^{x^2y+xy^2}g(x)f(y){\mid}{\leq}H_p(x,y)$. It is a generalization of the superstability theorem for the exponential functional equation proved by Baker.

• Journal of the Chungcheong Mathematical Society
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• v.19 no.4
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• pp.393-402
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• 2006

We investigate relations between multiplicity of solutions and source terms in a elliptic equation. We have a concerne with a sharp result for multiplicity of a nonlinear Laplacian differential equation.