Differentiable functions and their Fourier coefficients

2022 ◽  
Vol 0 (0) ◽  
Author(s):  
Vakhtang Tsagareishvili
Keyword(s):  
Bounded Variation ◽  
Fourier Coefficients ◽  
Special Series ◽  
Differentiable Functions ◽  
Derivatives Of

Abstract In the paper we consider the properties of Fourier coefficients of functions that possess derivatives of bounded variation. We investigate the convergence of the special series of Fourier coefficients with respect to general orthonormal systems (ONS). The obtained results are the best possible. We also describe the behavior of subsequences of general ONS.

scholarly journals Explicit, Determinantal, and Recurrent Formulas of Generalized Eulerian Polynomials

Axioms ◽  
2021 ◽  
Vol 10 (1) ◽  
pp. 37
Author(s):  
Yan Wang ◽  
Muhammet Cihat Dağli ◽  
Xi-Min Liu ◽  
Feng Qi
Keyword(s):  
General Formula ◽  
Bell Polynomials ◽  
Eulerian Polynomials ◽  
Differentiable Functions ◽  
Faà Di Bruno Formula ◽  
Derivatives Of

In the paper, by virtue of the Faà di Bruno formula, with the aid of some properties of the Bell polynomials of the second kind, and by means of a general formula for derivatives of the ratio between two differentiable functions, the authors establish explicit, determinantal, and recurrent formulas for generalized Eulerian polynomials.

scholarly journals Rate of Convergence for Ibragimov-Gadjiev-Durrmeyer Operators

2017 ◽  
Vol 50 (1) ◽  
pp. 119-129 ◽  
Author(s):  
Tuncer Acar
Keyword(s):  
Rate Of Convergence ◽  
Bounded Variation ◽  
General Class ◽  
Durrmeyer Operators ◽  
Special Cases ◽  
Derivatives Of

Abstract The present paper deals with the rate of convergence of the general class of Durrmeyer operators, which are generalization of Ibragimov-Gadjiev operators. The special cases of the operators include somewell known operators as particular cases viz. Szász-Mirakyan-Durrmeyer operators, Baskakov-Durrmeyer operators. Herewe estimate the rate of convergence of Ibragimov-Gadjiev-Durrmeyer operators for functions having derivatives of bounded variation.

scholarly journals A determinantal expression and a recursive relation of the Delannoy numbers

2021 ◽  
Vol 13 (2) ◽  
pp. 442-449 ◽  
Author(s):  
Feng Qi
Keyword(s):  
Recursive Relation ◽  
Differentiable Functions ◽  
Delannoy Numbers ◽  
Derivatives Of ◽  
Determinantal Expression

Abstract In the paper, by a general and fundamental, but non-extensively circulated, formula for derivatives of a ratio of two differentiable functions and by a recursive relation of the Hessenberg determinant, the author finds a new determinantal expression and a new recursive relation of the Delannoy numbers. Consequently, the author derives a recursive relation for computing central Delannoy numbers in terms of related Delannoy numbers.

Rank one property for derivatives of functions with bounded variation

1993 ◽  
Vol 123 (2) ◽  
pp. 239-274 ◽  
Author(s):  
Giovanni Alberti
Keyword(s):  
Bounded Variation ◽  
Measure Theory ◽  
Geometric Measure Theory ◽  
Geometric Measure ◽  
Rank One ◽  
Derivatives Of

SynopsisIn this paper we introduce a new tool in geometric measure theory and then we apply it to study the rank properties of the derivatives of vector functions with bounded variation.

scholarly journals Simultaneous Approximation for Generalized Srivastava-Gupta Operators

2015 ◽  
Vol 2015 ◽  
pp. 1-11 ◽  
Author(s):  
Tuncer Acar ◽  
Lakshmi Narayan Mishra ◽  
Vishnu Narayan Mishra
Keyword(s):  
Rate Of Convergence ◽  
Bounded Variation ◽  
Simultaneous Approximation ◽  
Integrable Functions ◽  
Derivatives Of

We introduce a new Stancu type generalization of Srivastava-Gupta operators to approximate integrable functions on the interval0,∞and estimate the rate of convergence for functions having derivatives of bounded variation. Also we present simultenaous approximation by new operators in the end of the paper.

DEFINITION AND CLASSIFICATION OF ONE-DIMENSIONAL CONTINUOUS FUNCTIONS WITH UNBOUNDED VARIATION

Fractals ◽  
2017 ◽  
Vol 25 (05) ◽  
pp. 1750048 ◽  
Author(s):  
Y. S. LIANG
Keyword(s):  
Fractal Dimension ◽  
Bounded Variation ◽  
Continuous Functions ◽  
Functions Of Bounded Variation ◽  
One Dimensional ◽  
Nondifferentiable Functions ◽  
Differentiable Functions ◽  
Closed Intervals ◽  
Bounded Variation Functions

The present paper mainly investigates the definition and classification of one-dimensional continuous functions on closed intervals. Continuous functions can be classified as differentiable functions and nondifferentiable functions. All differentiable functions are of bounded variation. Nondifferentiable functions are composed of bounded variation functions and unbounded variation functions. Fractal dimension of all bounded variation continuous functions is 1. One-dimensional unbounded variation continuous functions may have finite unbounded variation points or infinite unbounded variation points. Number of unbounded variation points of one-dimensional unbounded variation continuous functions maybe infinite and countable or uncountable. Certain examples of different one-dimensional continuous functions have been given in this paper. Thus, one-dimensional continuous functions are composed of differentiable functions, nondifferentiable continuous functions of bounded variation, continuous functions with finite unbounded variation points, continuous functions with infinite but countable unbounded variation points and continuous functions with uncountable unbounded variation points. In the end of the paper, we give an example of one-dimensional continuous function which is of unbounded variation everywhere.

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