• Communications of the Korean Mathematical Society
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• v.12 no.2
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• pp.403-403
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• 1997

• Journal of applied mathematics & informatics
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• v.28 no.3_4
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• pp.739-751
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• 2010

This article presents the result on existence, uniqueness and stability of mild solution of impulsive stochastic partial neutral functional differential equations under sufficient condition. The results are obtained by using the method of successive approximation.

• Nonlinear Functional Analysis and Applications
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• v.27 no.4
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• pp.807-812
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• 2022

The need for smoothness measures emerged by mathematicians working in the fields of approximation theory, functional analysis and real analysis. In the present paper, a new version of generalized modulus of smoothness is studied. The aim of defining that modulus, is to find the degree of best L_p functions approximation via trigonometric polynomials. We benefit from Jackson integrals to arrive to the essential approximation theorems.

• Journal of applied mathematics & informatics
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• v.41 no.4
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• pp.801-810
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• 2023

The aim of this paper, investigated of weighted space which contained the unbounded functions which is to be approximated by linear operators in terms some Well-known approximation tools such as the modulus of smoothness and K-functional. The characteristics of the identical theorem between modulus of smoothness and K-functional are consider. In addition to the establish the direct, converse and identical theorem by using some linear operators in terms modulus Ditzian-Totik.

• Kyungpook Mathematical Journal
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• v.62 no.3
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• pp.467-484
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• 2022

In this work, we define bivariate Bernstein-Kantorovich type operators on a triangular domain and obtain some approximation results for these operators. We start off by computing some moment estimates and prove a Korovkin type convergence theorem. Then, we estimate the rate of convergence using the partial and complete modulus of continuity, and derive a Voronovskaya-type asymptotic theorem. Further, we calculate the order of approximation with regard to the Peetre's K-functional and a Lipschitz type class. In addition, we construct the associated GBS type operators and compute the rate of approximation using the mixed modulus of continuity and class of the Lipschitz of Bögel continuous functions for these operators. Finally, we use the two operators to approximate example functions in order to compare their convergence.

• Korean Journal of Mathematics
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• v.30 no.3
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• pp.539-553
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• 2022

In the present paper, we aim to obtain several approximation properties of Stancu form Szász-Mirakjan-Durrmeyer operators based on Bézier basis functions with shape parameter λ ∈ [-1, 1]. We estimate some auxiliary results such as moments and central moments. Then, we obtain the order of convergence in terms of the Lipschitz-type class functions and Peetre's K-functional. Further, we prove weighted approximation theorem and also Voronovskaya-type asymptotic theorem. Finally, to see the accuracy and effectiveness of discussed operators, we present comparison of the convergence of constructed operators to certain functions with some graphical illustrations under certain parameters.

• Communications of the Korean Mathematical Society
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• v.31 no.4
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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.

• Kyungpook Mathematical Journal
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• v.43 no.4
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• pp.519-538
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• 2003

This paper delineates some fundamental properties of the set of strongly unique best coapproximation. Uniqueness of strongly unique best coapproximation is studied. Some characterizations of strongly unique best coapproximation and strongly unique best approximation are obtained. Some more results concerning strongly unique best uniform coapproximation and strongly unique best uniform approximation are presented. Some relations between best uniform approximation and strongly unique best uniform coapproximation are established.

• Bulletin of the Korean Mathematical Society
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• v.38 no.2
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• pp.293-302
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• 2001

We improve the greedy algorithm which is one of the general convergence criterion for certain iterative sequence in a given space by building a constructive greedy algorithm on a normed linear space using an arithmetic average of elements. We also show the degree of approximation order is still $Ο(1\sqrt{\n}$) by a bounded linear functional defined on a bounded subset of a normed linear space which offers a good approximation method for neural networks.

• Proceeding of EDISON Challenge
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• 2015.03a
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• pp.400-404
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• 2015

2차원 물질인 metal mono chalcogenides(MMC) 중 GaS와 GaSe를 대상으로 하여 층과 층 사이의 van der Waals(vdW) 상호작용을 density functional theory(DFT) 계산을 이용해 연구하였다. Local density approximation(LDA)와 generalized gradient approximation (GGA)의 두 가지 다른 exchange correlation functional을 이용하고, 또한 두 개의 층 사이에 작용하는 van der Waals 상호작용을 고려한 LDA-D2, GGA-D2 계산을 수행하였다. 이와 같은 네 가지 방법으로 층간거리를 바꾸어 binding energy curve를 계산하였다. 그 결과 GGA-D2계산이 MMC의 층간 상호 작용을 가장 잘 기술하였다.