Correction to: Degenerate Bernstein polynomials

In this paper, we investigate some properties and identities for fully degenerate Bernoulli polynomials in connection with degenerate Bernstein polynomials by means of bosonic p-adic integrals on Z p and generating functions. Furthermore, we study two variable degenerate Bernstein polynomials and the degenerate Bernstein operators.

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Some Identities on Degenerate Bernstein and Degenerate Euler Polynomials

Mathematics ◽

10.3390/math7010047 ◽

2019 ◽

Vol 7 (1) ◽

pp. 47 ◽

Cited By ~ 4

Author(s):

Taekyun Kim ◽

Dae San Kim

Keyword(s):

Differential Equations ◽

Generating Functions ◽

Bernstein Polynomials ◽

Umbral Calculus ◽

Euler Polynomials ◽

Euler Numbers ◽

Euler Numbers And Polynomials ◽

Special Numbers And Polynomials ◽

Degenerate Bernstein Polynomials ◽

Combinatorial Methods

In recent years, intensive studies on degenerate versions of various special numbers and polynomials have been done by means of generating functions, combinatorial methods, umbral calculus, p-adic analysis and differential equations. The degenerate Bernstein polynomials and operators were recently introduced as degenerate versions of the classical Bernstein polynomials and operators. Herein, we firstly derive some of their basic properties. Secondly, we explore some properties of the degenerate Euler numbers and polynomials and also their relations with the degenerate Bernstein polynomials.

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A note on degenerate Bernstein polynomials

Journal of Inequalities and Applications ◽

10.1186/s13660-019-2071-1 ◽

2019 ◽

Vol 2019 (1) ◽

Cited By ~ 3

Author(s):

Taekyun Kim ◽

Dae San Kim ◽

Gwan-Woo Jang ◽

Jongkyum Kwon

Keyword(s):

Bernstein Polynomials ◽

Degenerate Bernstein Polynomials

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Unified Degenerate Central Bell Polynomials

10.20944/preprints201908.0213.v1 ◽

2019 ◽

Author(s):

Mehmet Acikgoz ◽

Ugur Duran

Keyword(s):

Explicit Formula ◽

Bernstein Polynomials ◽

Summation Formula ◽

Bell Polynomials ◽

Genocchi Numbers ◽

Central Factorial Numbers ◽

Degenerate Bernstein Polynomials

In this paper, we firstly consider extended degenerate central factorial numbers of the second kind and provide some properties of them. We then introduce unified degenerate central Bell polynomials and numbers and investigate many relations and formulas including summation formula, explicit formula and derivative property. Moreover, we derive several correlations for the fully degenerate central Bell polynomials associated with the degenerate Bernstein polynomials and the degenerate Bernoulli, Euler and Genocchi numbers.

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A Note on Degenerate Bernstein and Degenerate Euler Polynomials

10.20944/preprints201807.0182.v1 ◽

2018 ◽

Author(s):

Taekyun Kim ◽

Dae San Kim

Keyword(s):

Bernstein Polynomials ◽

Euler Polynomials ◽

Euler Numbers ◽

Euler Numbers And Polynomials ◽

Degenerate Bernstein Polynomials

In this paper, we investigate the recently introduced degenerate Bernstein polynomials and operators and derive some of their properties. Also, we give some properties of the degenerate Euler numbers and polynomials and their connection with the degenerate Euler polynomials.

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The Powers and their Bernstein Polynomials

Real Analysis Exchange ◽

10.2307/44153570 ◽

1983 ◽

Vol 9 (2) ◽

pp. 578

Author(s):

Keyword(s):

Bernstein Polynomials

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Numerical Analysis of Viscoelastic Rotating Beam with Variable Fractional Order Model Using Shifted Bernstein–Legendre Polynomial Collocation Algorithm

Fractal and Fractional ◽

10.3390/fractalfract5010008 ◽

2021 ◽

Vol 5 (1) ◽

pp. 8

Author(s):

Cundi Han ◽

Yiming Chen ◽

Da-Yan Liu ◽

Driss Boutat

Keyword(s):

Numerical Analysis ◽

Fractional Order ◽

Governing Equation ◽

Numerical Solutions ◽

Bernstein Polynomials ◽

Matrix Product ◽

Algebraic Equations ◽

Rotating Beam ◽

The Matrix ◽

The Time Domain

This paper applies a numerical method of polynomial function approximation to the numerical analysis of variable fractional order viscoelastic rotating beam. First, the governing equation of the viscoelastic rotating beam is established based on the variable fractional model of the viscoelastic material. Second, shifted Bernstein polynomials and Legendre polynomials are used as basis functions to approximate the governing equation and the original equation is converted to matrix product form. Based on the configuration method, the matrix equation is further transformed into algebraic equations and numerical solutions of the governing equation are obtained directly in the time domain. Finally, the efficiency of the proposed algorithm is proved by analyzing the numerical solutions of the displacement of rotating beam under different loads.

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