Interpolation and <mml:math altimg="si1.gif" display="inline" overflow="scroll" xmlns:xocs="http://www.elsevier.com/xml/xocs/dtd" xmlns:xs="http://www.w3.org/2001/XMLSchema" xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance" xmlns="http://www.elsevier.com/xml/ja/dtd" xmlns:ja="http://www.elsevier.com/xml/ja/dtd" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:tb="http://www.elsevier.com/xml/common/table/dtd" xmlns:sb="http://www.elsevier.com/xml/common/struct-bib/dtd" xmlns:ce="http://www.elsevier.com/xml/common/dtd" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns:cals="http://www.elsevier.com/xml/common/cals/dtd"><mml:msub><mml:mrow><mml:mi>L</mml:mi></mml:mrow><mml:mrow><mml:mn>1</mml:mn></mml:mrow></mml:msub></mml:math>-approximation by trigonometric polynomials and blending functions

Fractal interpolation is an advance technique for visualization of scientific shaped data. In this paper, we present a new family of partially blended rational cubic trigonometric fractal interpolation surfaces (RCTFISs) with a combination of blending functions and univariate rational trigonometric fractal interpolation functions (FIFs) along the grid lines of the interpolation domain. The developed FIFs use rational trigonometric functions [Formula: see text], where [Formula: see text] and [Formula: see text] are cubic trigonometric polynomials with four shape parameters. The convergence analysis of partially blended RCTFIS with the original surface data generating function is discussed. We derive sufficient data-dependent conditions on the scaling factors and shape parameters such that the fractal grid line functions lie above the grid lines of a plane [Formula: see text], and consequently the proposed partially blended RCTFIS lies above the plane [Formula: see text]. Positivity preserving partially blended RCTFIS is a special case of the constrained partially blended RCTFIS. Numerical examples are provided to support the proposed theoretical results.

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Approximation of Unbounded Functions by Trigonometric Polynomials

Diyala Journal for Pure Science ◽

10.24237/djps.1304.319b ◽

2017 ◽

Vol 13 (4) ◽

pp. 106-116

Author(s):

Alaa A. Auad ◽

◽

Mousa M. Khrajan

Keyword(s):

Trigonometric Polynomials

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Approximate Solution Of A Singular Integral Equation With A Multiplicative Cauchy Kernel In The Half-Plane

Computational Methods in Applied Mathematics ◽

10.2478/cmam-2008-0010 ◽

2008 ◽

Vol 8 (2) ◽

pp. 143-154 ◽

Cited By ~ 1

Author(s):

P. KARCZMAREK

Keyword(s):

Integral Equation ◽

Approximate Solution ◽

Singular Integral Equation ◽

Half Plane ◽

Singular Integral ◽

Trigonometric Polynomials ◽

Cauchy Kernel

AbstractIn this paper, Jacobi and trigonometric polynomials are used to con-struct the approximate solution of a singular integral equation with multiplicative Cauchy kernel in the half-plane.

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Approximation of Ω—bandlimited Functions by Ω—bandlimited Trigonometric Polynomials

Sampling Theory, Signal Processing, and Data Analysis ◽

10.1007/bf03549477 ◽

2007 ◽

Vol 6 (3) ◽

pp. 273-296 ◽

Cited By ~ 2

Author(s):

R. Martin

Keyword(s):

Trigonometric Polynomials ◽

Bandlimited Functions

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An extension of q-starlike and q-convex error functions endowed with the trigonometric polynomials

Mathematica Slovaca ◽

10.1515/ms-2017-0374 ◽

2020 ◽

Vol 70 (3) ◽

pp. 599-604

Author(s):

Şahsene Altinkaya

Keyword(s):

Error Function ◽

Trigonometric Polynomials ◽

Error Functions ◽

The Family ◽

Coefficient Inequalities

AbstractIn this present investigation, we will concern with the family of normalized analytic error function which is defined by$$\begin{array}{} \displaystyle E_{r}f(z)=\frac{\sqrt{\pi z}}{2}\text{er} f(\sqrt{z})=z+\overset{\infty }{\underset {n=2}{\sum }}\frac{(-1)^{n-1}}{(2n-1)(n-1)!}z^{n}. \end{array}$$By making the use of the trigonometric polynomials Un(p, q, eiθ) as well as the rule of subordination, we introduce several new classes that consist of 𝔮-starlike and 𝔮-convex error functions. Afterwards, we derive some coefficient inequalities for functions in these classes.

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Degree of best approximation by trigonometric blending functions

Mathematische Zeitschrift ◽

10.1007/bf01246949 ◽

1985 ◽

Vol 189 (1) ◽

pp. 143-150 ◽

Cited By ~ 13

Author(s):

Werner Hau�mann ◽

Kurt Jetter ◽

Bernd Steinhaus

Keyword(s):

Best Approximation ◽

Blending Functions

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SOME ESTIMATES FOR POLYNOMIALS

Asian-European Journal of Mathematics ◽

10.1142/s1793557109000352 ◽

2009 ◽

Vol 02 (03) ◽

pp. 425-434

Author(s):

Tatsuhiro Honda ◽

Mitsuhiro Miyagi ◽

Masaru Nishihara ◽

Seiko Ohgai ◽

Mamoru Yoshida

Keyword(s):

Trigonometric Polynomials ◽

Alternative Proof ◽

Bernstein Inequalities

We give an elementary alternative proof of the Bernstein inequalities and the Szegö inequalities for trigonometric polynomials or polynomials.

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Approximation by trigonometric polynomials in the framework of variable exponent grand Lebesgue spaces

Georgian Mathematical Journal ◽

10.1515/gmj-2015-0059 ◽

2016 ◽

Vol 23 (1) ◽

Cited By ~ 2

Author(s):

Nina Danelia ◽

Vakhtang Kokilashvili

Keyword(s):

Lebesgue Space ◽

Variable Exponent ◽

Trigonometric Polynomials ◽

Lebesgue Spaces ◽

Variable Exponent Lebesgue Space ◽

Grand Lebesgue Spaces ◽

Direct And Inverse Theorems ◽

Inverse Theorems ◽

Grand Lebesgue Space

AbstractIn this paper we establish direct and inverse theorems on approximation by trigonometric polynomials for the functions of the closure of the variable exponent Lebesgue space in the variable exponent grand Lebesgue space.

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