• East Asian mathematical journal
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• v.28 no.5
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• pp.533-541
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• 2012

A common fixed point result of Gregus type for subcompatible mappings defined on a complete linear metric space is obtained. The considered underlying space is generalized from Banach space to complete linear metric spaces, which include Banach space and complete metrizable locally convex spaces. Invariant approximation results have also been determined as its application.

• Journal of the Korean Society for Industrial and Applied Mathematics
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• v.9 no.2
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• pp.99-106
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• 2005

We present a relation between the orthogonality of the constrained Legendre polynomials over the triangular domain and the BB ($B{\acute{e}zier}\;-Bernstein$) coefficients of the polynomials using the equivalence of orthogonal complements. Using it we also show that the best constrained degree reduction of polynomials in BB form equals the best approximation of weighted Euclidean norm of coefficients of given polynomial in BB form from the coefficients of polynomials of lower degree in BB form.

• Communications of the Korean Mathematical Society
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• v.12 no.3
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• pp.619-629
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• 1997

In this paper, we give some properties of the sets $D_z(x_o, G)P_{G, z}(x)$. We also provide the relation between $P_{G, z}(x)$ and G$\hat{a}$teaux derivatives.

• Bulletin of the Korean Mathematical Society
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• v.25 no.2
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• pp.267-273
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• 1988

• Bulletin of the Korean Mathematical Society
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• v.43 no.2
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• pp.377-387
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• 2006

In this paper, some characterizations of representation for continuous linear functionals on $2{\kappa}$-inner product spaces in terms of best approximations and orthogonalities are given.

• Steel and Composite Structures
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• v.8 no.5
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• pp.343-359
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• 2008

In the present study, an efficient method for the optimum design of three-dimensional (3D) steel framed structures is proposed. In this method, in addition to choosing the best position of columns based on architectural requirements, the optimum cross-sectional dimensions of elements are determined. The preliminary design variables are considered as the number of columns in structural plan, which are determined by a direct optimization method suitable for discrete variables, without requiring the evaluation of derivatives. After forming the geometry of structure, the main variables of the cross-sectional dimensions are evaluated, which satisfy the design constraints and also achieve the least-weight of the structure. To reduce the number of finite element analyses and the overall computational time, a new third order approximate function is introduced which employs only the diagonal elements of the higher order derivatives matrices. This function produces a high quality approximation and also, a robust optimization process. The main feature of the proposed techniques that the higher order derivatives are established by the first order exact derivatives. Several examples are solved and efficiency of the new approximation method and also, the proposed method for the best position of columns in 3D steel framed structures is discussed.

• Bulletin of the Korean Mathematical Society
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• v.34 no.2
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• pp.259-271
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• 1997

Let K be a nonempty subset of a normed linear space X and let x $\in$ X. An element k$_0$ in K satisfying $\$\mid$$x - k$_0$$\$\mid$$ = d(x, K) := (equation omitted) $\$\mid$$x - k$\$\mid$$ is called a best approximation to x from K. For any x $\in$ X, the set of all best approximations to x from K is denoted by P$_K$(x) = {k $\in$ K : $\$\mid$$ x - k $\$\mid$$ = d(x, K)}. (omitted)

• Journal of the Korean Mathematical Society
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• v.45 no.5
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• pp.1297-1310
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• 2008

Main purpose of this paper is to combine the optimal form of Fan's best approximation theorem and Nash's equilibrium existence theorem into a single existence theorem simultaneously. For this, we first prove a general best proximity pair theorem which includes a number of known best proximity theorems. Next, we will introduce a new equilibrium concept for a generalized Nash game with normal form, and as applications, we will prove new existence theorems of Nash equilibrium pairs for generalized Nash games with normal form.

• 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.

• The Mathematical Education
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• v.23 no.2
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• pp.51-53
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• 1985