• Journal of applied mathematics & informatics
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• 제41권4호
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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.

• Nonlinear Functional Analysis and Applications
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• 제27권4호
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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.

• 대한전기학회논문지:전기물성ㆍ응용부문C
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• 제54권10호
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• pp.443-448
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• 2005

To measure modulus, damping properties and smoothness of semiconducting materials in power cable, we have investigated those of semiconducting materials showed by changing the content of carbon black. Then they were produced as sheets after pressing for 20 minutes at 180[$^{\circ}C$] with a pressure of 200[kg/cm$^{2}$]. The content of conductive carbon black was the variable, and their contents were 20, 30 and 40[wt$\%$], respectively. The modulus and tans were measured by DMA 2980. The ranges of measurement temperature were from -50[$^{\circ}C$] to 100[$^{\circ}C$] and measurement frequency was 1[Hz3. The modulus of specimens was increased according to a increment of a carbon black content. And modulus was rapidly decreased at the glass transition temperature. The tans of specimens was decreased according to a increment of a carbon black content. The smoothness was measured by JSM-6400. EEA resin from SEM measurement was best the dispersion of carbon back in base resin.

• Journal of applied mathematics & informatics
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• 제24권1_2호
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• pp.343-355
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• 2007

Using the modulus of smoothness ${\omega}^2_{{\varphi}^{\lambda}(f,t)_{\omega}$ Stechkin-Marchaud-Type inequalities with Jacobi weights of Bernstein Operators is established.

• Korean Journal of Mathematics
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• 제25권1호
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• pp.99-116
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• 2017

The aim of this article is to introduce a new form of Kantorovich $Sz{\acute{a}}sz$-type operators involving Charlier polynomials. In this manuscript, we discuss the rate of convergence, better error estimates. Further, we investigate order of approximation in the sense of local approximation results with the help of Ditzian-Totik modulus of smoothness, second order modulus of continuity, Peetre's K-functional and Lipschitz class.

• Fibers and Polymers
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• 제3권4호
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• pp.169-173
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• 2002

Fabric touch was evaluated psychophysically in order to determine the relationship between mechanical properties and subjective sensation. For subjective touch sensation, eight aspects such as hardness, smoothness, coarseness, coolness, pliability, crispness, heaviness and thickness were evaluated using free modulus magnitude estimation (FEME) technique. KES-FB was used to measure the mechanical properties of fabrics. Woolen fabric with the highest values of WC and weight was evaluated as the coarsest, heaviest and thickest. While silk crepe do chine with the lowest LT, G, 2HG, thickness and weight was rated as smoother and more pliable than any other fabrics. And flax with the highest values of LT and SMD was evaluated as hard, cool and crisp. Fabric touch and satisfaction were predicted well from the mechanical properties, especially from SMD, by regression analysis. Satisfaction for touch increased as smoothness increased.

• 대한수학회보
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• 제52권2호
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• pp.593-601
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• 2015

Let $f{\in}C^r$ ([-1,1]), $r{\geq}0$ and let $L^*$ be a linear left fractional differential operator such that $L^*$ $(f){\geq}0$ throughout [0, 1]. We can find a sequence of polynomials $Q_n$ of degree ${\leq}n$ such that $L^*$ $(Q_n){\geq}0$ over [0, 1], furthermore f is approximated left fractionally and simulta-neously by $Q_n$ on [-1, 1]. The degree of these restricted approximations is given via inequalities using a higher order modulus of smoothness for $f^{(r)}$.

• Kyungpook Mathematical Journal
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• 제27권2호
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• pp.173-179
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• 1987

In this article the absolute convergence of lacunary Fourier Coefficients Series is studied for Hilbert space valued functions. The considered functions arc assumed to be of either the modulus of continuity or the modulus of smoothness of order l which are considered only at a fixed point in [$-{\pi},{\pi}$]. On the other hand for values in weakly sequentially complete Banach space, the lacunary Fourier coefficients series is strongly unconditionally convergent. The results obtained here are a kind of a generalization of the results due to Kandil [4].

• 대한수학회보
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• 제30권2호
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• pp.201-212
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• 1993

It is our purpose in this paper to first establish an inequality in real uniformly smooth Banach spaces with modulus of smoothness of power type q > 1 that generalizes a well known Hilbert space inequality. Using our inequality, we shall then extend the above result of Qihou [15] on the Ishikawa iteration process from Hilbert spaces to these much more general Banach spaces. Furthermore, we shall prove that the Mann iteration process converges strongly to the unique fixed point of a quasi-contractive map in this general setting. No compactness assumption on K is required in our theorems.

• 대한수학회논문집
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• 제34권2호
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• pp.465-475
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• 2019

Let X be a Banach space and $X^*$ be its dual. In this paper, we give relationships among some parameters in $X^*$: ${\varepsilon}$-nonsquareness parameter, $J({\varepsilon},X^*)$; ${\varepsilon}$-boundary parameter, $Q({\varepsilon},X^*)$; the modulus of smoothness, ${\rho}_{X^*}({\varepsilon})$; and ${\varepsilon}$-Pythagorean parameter, $E({\varepsilon},X^*)$, and weak orthogonality parameter, ${\omega}(X)$ in X that imply uniform norm structure in X. Some existing results are extended or approved.