• East Asian mathematical journal
• /
• v.34 no.5
• /
• pp.693-702
• /
• 2018

In this paper, we consider the generalized Hyers-Ulam stability for the following additive-quadratic functional equation with involution $f(x+2y)-f(2x+y)+f(x+y)+f({\sigma}(x)+y)+f(x)-4f(y)-f({\sigma}(y))=0$ in non-Archimedean spaces.

• Journal of the Chungcheong Mathematical Society
• /
• v.28 no.2
• /
• pp.321-330
• /
• 2015

In this paper, we prove the generalized Hyers-Ulam stability for the following additive-quadratic functional equation f(2x + y) + f(2x - y) = f(x + y) + f(x - y) + 4f(x) + 2f(-x) in modular spaces by using a fixed point theorem for modular spaces.

• Journal of the Korean Statistical Society
• /
• v.32 no.1
• /
• pp.11-20
• /
• 2003

Let｛Ｘt｝be an m-dimensional linear process of the form (equation omitted), where｛Zt｝is a sequence of stationary m-dimensional weakly associated random vectors with EZt = O and E∥Zt∥$^2$＜$\infty$. We Prove central limit theorems for multivariate linear processes generated by weakly associated random vectors. Our results also imply a functional central limit theorem.

• Journal of applied mathematics & informatics
• /
• v.37 no.1_2
• /
• pp.53-63
• /
• 2019

In this paper, we show the existence of solution of the neutral stochastic functional differential equations under non-Lipschitz condition, a weakened linear growth condition and a contractive condition. Furthermore, in order to obtain the existence of solution to the equation we used the Picard sequence.

• Journal of the Chungcheong Mathematical Society
• /
• v.26 no.2
• /
• pp.377-391
• /
• 2013

The main goal of this paper is to present the additional stability results of the following orthogonally additive and orthogonally quadratic functional equation $$f(\frac{x}{2}+y)+f(\frac{x}{2}-y)+f(\frac{x}{2}+z)+f(\frac{x}{2}-z)=\frac{3}{2}f(x)-\frac{1}{2}f(-x)+f(y)+f(-y)+f(z)+f(-z)$$ for all $x,y,z$ with $x{\bot}y$, which has been introduced in the paper [11], in orthogonality Banach spaces and in non-Archimedean orthogonality Banach spaces.

• Journal of Korean Society on Water Environment
• /
• v.33 no.6
• /
• pp.744-753
• /
• 2017

The sediment delivery ratio (SDR) is widely used to estimate sediment loads by multiplying soil loss through the Revised Universal Equation (RUSLE). In this study, the SDR equation was developed for the Lake Imha watershed using soil loss calculated by RUSLE and sediment loads by the calibrated Hydrological Simulation. Program Fortran (HSPF). The ratio of watershed relief and channel length ($R_f/L_{ch}$), the ratio of watershed relief and watershed length ($R_f/L_b$), curve number (CN), area (A), and channel slope ($SLP_{ch}$) demonstrated strong correlations with SDR. SDR equations were developed by a combination of subwatershed parameters by referring to the correlation analysis. The area based power functional SDR developed in this study showed significant errors at the point right after entering major tributaries, because SDR was unrealistically reduced when the watershed area increased significantly. The $SLP_{ch}$-based power functional SDR also showed extraordinary values when the channel slope was gradual. The SDR equation that showed the highest value of the coefficient of determination also presented unrealistic changes in the sediment loads within a relatively short river distance. The SDR equation $SDR=0.0003A^{0.198}R_f/L{_w}^{1.167}$ was recommended for application to the Lake Imha watershed. Using this equation, sediment loads at the outlet of the Lake Imha watershed were calculated, and the HSPF parameters related to sediment in the uncalibrated subwatersheds were determined by referring to the sediment loads calculated with the SDR equation.

• Korean Journal of Mathematics
• /
• v.20 no.2
• /
• pp.213-223
• /
• 2012

In this paper, we will prove the superstability of the following generalized Pexider type exponential equation $${f(x+y)}^m=g(x)h(y)$$, where $f,g,h\;:\;G{\rightarrow}\mathbb{R}$ are unknown mappings and $m$ is a fixed positive integer. Here G is an Abelian group (G, +), and $\mathbb{R}$ the set of real numbers. Also we will extend the obtained results to the Banach algebra. The obtained results are generalizations of P. G$\check{a}$vruta's result in 1994 and G. H. Kim's results in 2011.

• Journal of the Korean Society for Industrial and Applied Mathematics
• /
• v.26 no.4
• /
• pp.333-342
• /
• 2022

In this paper, we perform a direct comparison study of real experimental data for domain rearrangement and the Cahn-Hilliard (CH) equation on the dynamics of morphological evolution. To validate a mathematical model for physical phenomena, we take initial conditions from experimental images by using an image segmentation technique. The image segmentation algorithm is based on the Mumford-Shah functional and the Allen-Cahn (AC) equation. The segmented phase-field profile is similar to the solution of the CH equation, that is, it has hyperbolic tangent profile across interfacial transition region. We use unconditionally stable schemes to solve the governing equations. As a test problem, we take domain rearrangement of lipid bilayers. Numerical results demonstrate that comparison of the evolutions with experimental data is a good benchmark test for validating a mathematical model.

• Journal of applied mathematics & informatics
• /
• v.33 no.3_4
• /
• pp.435-445
• /
• 2015

In this paper, using the fixed point method, we investigate the generalized Hyers-Ulam stability of the system of quintic functional equation $f(x_1+x_2,y)+f(x_1-x_2,y)=2f(x_1,y)+2f(x_2,y)\;f(x,2_{y1}+y_2)+f(x,2_{y1}-y_2)=f(x,y_1-2_{y2})+f(x,y_1+y_2)\;-f(x,y_1-y_2)+15f(x,y_1)+6f(x,y_2)$ in non-Archimedean 2-Banach spaces.

• Bulletin of the Korean Mathematical Society
• /
• v.43 no.4
• /
• pp.703-709
• /
• 2006

Let X, Y be vector spaces. It is shown that if an even mapping $f:X{\rightarrow}Y$ satisfies f(0) = 0 and $$(0.1)\;f(\frac {x+y} 2+z)+f(\frac {x+y} 2-z)+f(\frac {x-y} 2+z)+f(\frac {x-y} 2-z)=f(x)+f(y)+4f(z)$$ for all x, y, z ${\in}$X, then the mapping $f:X{\rightarrow}Y$ is quadratic. Furthermore, we prove the Cauchy-Rassias stability of the functional equation (0.1) in Banach spaces.