• Journal of applied mathematics & informatics
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• 제36권1_2호
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• pp.1-14
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• 2018

In this paper, we prove the existence, uniqueness and stability of solution for some nonlinear functional-integral equations by using generalized coupled Lipschitz condition. We prove a fixed point theorem to obtain the mentioned aim in Banach space $X=C([a,b],{\mathbb{R}})$. As application we study some volterra integral equations with linear, nonlinear and single kernel.

• 충청수학회지
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• 제33권3호
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• pp.351-363
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• 2020

We introduce a new concept of Stepanov weighted pseudo almost periodic functions of class r which have been established by recently in [20]. Furthermore, we study the uniqueness and existence of Stepanov weighted pseudo almost periodic mild solutions of partial neutral functional differential equations having the Stepanov pseudo almost periodic forcing terms on finite delay.

• 한국수학교육학회지시리즈B:순수및응용수학
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• 제16권3호
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• pp.297-306
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• 2009

In this paper, we obtain the general solution and the generalized HyersUlam stability theorem for an additive functional equation $af(x+y)+2f({\frac{x}{2}}+y)+2f(x+{\frac{y}{2})=(a+3)[f(x)+f(y)]$for any fixed integer a.

• 호남수학학술지
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• 제32권2호
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• pp.193-202
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• 2010

We investigate the estimation of the moisture transfer coefficients in porous media by optimization technique which minimizes the functional defined by the squares error of the numerical solution of an inverse diffusion problem from their experimental values of the moisture content at the some time-steps. In this paper, we solve a diffusion equation numerically by the control volume finite element methods.

• Journal of the Korean Society for Industrial and Applied Mathematics
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• 제26권4호
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• pp.333-342
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• 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.

• 대한수학회보
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• 제45권3호
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• pp.587-600
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• 2008

In this paper we establish the general solution and investigate the Hyers-Ulam-Rassias stability of the following functional equation in quasi-Banach spaces. $${\sum\limits_{{{1{\leq}i<j{\leq}4}\limits_{1{\leq}k<l{\leq}4}}\limits_{k,l{\in}I_{ij}}}\;f(x_i+x_j-x_k-x_l)=2\;\sum\limits_{1{\leq}i<j{\leq}4}}\;f(x_i-x_j)$$ where $I_{ij}$={1, 2, 3, 4}\backslash${i, j} for all $1{\leq}i<j{\leq}4$. The concept of Hyers-Ulam-Rassias stability originated from Th. M. Rassias' stability theorem that appeared in his paper: On the stability of the linear mapping in Banach spaces, Proc. Amer. Math. Soc.

• Korean Journal of Mathematics
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• 제30권2호
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• pp.205-229
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• 2022

The aim of this paper is to obtain some results which belong to fixed point theory such as strong convergence, rate of convergence, stability, and data dependence by using the new Jungck-type iteration method for a mapping defined in complex-valued Banach spaces. In addition, some of these results are supported by nontrivial numerical examples. Finally, it is shown that the sequence obtained from the new iteration method converges to the solution of the functional integral equation in complex-valued Banach spaces. The results obtained in this paper may be interpreted as a generalization and improvement of the previously known results.

• 충청수학회지
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• 제26권4호
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• pp.757-767
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• 2013

We investigate the general solution of the following functional equation and the generalized Hyers-Ulam-Rassias stability problem in quasi ${\beta}$-normed spaces and then the stability by using alternative fixed point method for the following quintic function $f:X{\rightarrow}Y$ such that f(3x+y)+f(3x-y)+5[f(x+y)+f(x-y)]=4[f(2x+y)+f(2x-y)]+2f(3x)-246f(x), for all $x,y{\in}X$.

• Nonlinear Functional Analysis and Applications
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• 제26권2호
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• pp.303-322
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• 2021

The concepts of new classes of mappings are introduced in the spaces which are more general space than the usual metric spaces. The existence and uniqueness of common fixed points and fixed point results are established in the setting of complete complex valued b-metric spaces. An illustration is given by establishing the existence of solution of periodic differential equations in the framework of a complete complex valued b-metric spaces.

• Nonlinear Functional Analysis and Applications
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• 제27권3호
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• pp.679-689
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• 2022

In this paper, we establish sufficient conditions for the existence and uniqueness of solution for a class of initial boundary value problems with Dirichlet condition in regard to a category of fractional-order partial differential equations. The results are established by a method based on the theorem of Lax Milligram.