Exact Constant in Dzyadyk’s Inequality for the Derivative of an Algebraic Polynomial

2017 ◽  
Vol 69 (5) ◽  
pp. 725-733 ◽  
Author(s):  
V. D. Halan ◽  
I. O. Shevchuk
Keyword(s):  
Algebraic Polynomial ◽  
Exact Constant

Algebraic Polynomial Based Topological Study of Graphite Carbon Nitride (g-) Molecular Structure.

2021 ◽  
pp. 1-22
Author(s):  
Abdul Rauf ◽  
Muhammad Ishtiaq ◽  
Mehwish Hussain Muhammad ◽  
Muhammad Kamran Siddiqui ◽  
Qammar Rubbab
Keyword(s):  
Molecular Structure ◽  
Algebraic Polynomial ◽  
Carbon Nitride

scholarly journals Approximation by Boolean sums of linear operators: Telyakovskiǐ-type estimates

1990 ◽  
Vol 42 (2) ◽  
pp. 253-266 ◽  
Author(s):  
Jia-Ding Cao ◽  
Heinz H. Gonska
Keyword(s):  
Upper Bound ◽  
Algebraic Polynomial ◽  
Present Note ◽  
Type Inequality ◽  
Linear Operators ◽  
Polynomial Operators ◽  
Boolean Sums ◽  
General Conditions

In the present note we study the question: “Under which general conditions do certain Boolean sums of linear operators satisfy Telyakovskiǐ-type estimates?” It is shown, in particular, that any sequence of linear algebraic polynomial operators satisfying a Timan-type inequality can be modified appropriately so as to obtain the corresponding upper bound of the Telyakovskiǐ-type. Several examples are included.

Algebraic Polynomial Identities

2010 ◽  
pp. 271-294
Author(s):  
Charles Chui ◽  
Johan de Villiers
Keyword(s):  
Algebraic Polynomial ◽  
Polynomial Identities

scholarly journals Deterministic and random approximation by the combination of algebraic polynomials and trigonometric polynomials

2021 ◽  
Vol 19 (1) ◽  
pp. 1047-1055
Author(s):  
Zhihua Zhang
Keyword(s):  
Fourier Series ◽  
Trigonometric Polynomial ◽  
Algebraic Polynomial ◽  
Fourier Coefficients ◽  
Random Processes ◽  
Qualitative Theory ◽  
Trigonometric Polynomials ◽  
Algebraic Polynomials ◽  
Fourier Approximation ◽  
Random Differential Equations

Abstract Fourier approximation plays a key role in qualitative theory of deterministic and random differential equations. In this paper, we will develop a new approximation tool. For an m m -order differentiable function f f on [ 0 , 1 0,1 ], we will construct an m m -degree algebraic polynomial P m {P}_{m} depending on values of f f and its derivatives at ends of [ 0 , 1 0,1 ] such that the Fourier coefficients of R m = f − P m {R}_{m}=f-{P}_{m} decay fast. Since the partial sum of Fourier series R m {R}_{m} is a trigonometric polynomial, we can reconstruct the function f f well by the combination of a polynomial and a trigonometric polynomial. Moreover, we will extend these results to the case of random processes.

Estimate of the derivative of an algebraic polynomial

1990 ◽  
Vol 47 (3) ◽  
pp. 275-277
Author(s):  
A. A. Pekarskii
Keyword(s):  
Algebraic Polynomial

scholarly journals Concentration of the error between a function and its polynomial of best uniform approximation

1998 ◽  
Vol 41 (3) ◽  
pp. 447-463 ◽  
Author(s):  
Maurice Hasson
Keyword(s):  
Uniform Approximation ◽  
Algebraic Polynomial ◽  
General Class ◽  
Supremum Norm ◽  
Best Uniform Approximation ◽  
Class A ◽  
Image Position ◽  
Class Of Functions

Let f be a continuous real valued function defined on [−1, 1] and let En(f) denote the degree of best uniform approximation to f by algebraic polynomial of degree at most n. The supremum norm on [a, b] is denoted by ∥.∥[a, b] and the polynomial of degree n of best uniform approximation is denoted by Pn. We find a class of functions f such that there exists a fixed a ∈(−1, 1) with the following propertyfor some positive constants C and N independent of n. Moreover the sequence is optimal in the sense that if is replaced by then the above inequality need not hold no matter how small C > 0 is chosen.We also find another, more general class a functions f for whichinfinitely often.

scholarly journals On the exact constant in the quantitative Steinitz theorem in the plane

1994 ◽  
Vol 12 (4) ◽  
pp. 387-398 ◽  
Author(s):  
I. Bárány ◽  
A. Heppes
Keyword(s):  
Exact Constant
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