scholarly journals On Bleimann-Butzer-Hahn operators for exponential functions

2007 ◽  
Vol 75 (3) ◽  
pp. 409-415 ◽  
Author(s):  
Ulrich Abel ◽  
Mircea Ivan
Keyword(s):  
Exponential Type ◽  
Binomial Coefficients ◽  
Monotone Functions ◽  
Exponential Functions ◽  
Approximation Process

Some inequalities involving the binomial coefficients are obtained. They are used to determine the domain of convergence of the Bleimann, Butzer and Hahn approximation process for exponential type functions. An answer to Hermann's conjecture related to the Bleimann, Butzer and Hahn operators for monotone functions is given.

scholarly journals Exponential moments and simultaneous approximation properties for Durrmeyer type operators with weights of Szasz basis functions

Filomat ◽  
2021 ◽  
Vol 35 (5) ◽  
pp. 1465-1475
Author(s):  
Antonio-Jesús López-Moreno ◽  
Vijay Gupta
Keyword(s):  
Exponential Type ◽  
Exponential Growth ◽  
Simultaneous Approximation ◽  
Basis Functions ◽  
Approximation Properties ◽  
Exponential Functions ◽  
Quantitative Estimates ◽  
Exponential Moments ◽  
Durrmeyer Type Operators ◽  
Derivatives Of

The present paper deals with the approximation properties for exponential functions of general Durrmeyer type operators having the weights of Sz?sz basis functions. Here we give explicit expressions for exponential type moments by means of which we establish, for the derivatives of the operators, the Voronovskaja formulas for functions of exponential growth and the corresponding weighted quantitative estimates for the remainder in simultaneous approximation.

scholarly journals Convergence estimates of a family of approximation operators of exponential type

Filomat ◽  
2020 ◽  
Vol 34 (13) ◽  
pp. 4329-4341
Author(s):  
Vijay Gupta ◽  
Manuel López-Pellicer ◽  
H.M. Srivastava
Keyword(s):  
Asymptotic Formula ◽  
Modulus Of Continuity ◽  
Exponential Type ◽  
Exponential Growth ◽  
Simultaneous Approximation ◽  
Type Result ◽  
Exponential Functions ◽  
Approximation Operators ◽  
Convergence Estimates

The main object of this article is to consider a family of approximation operators of exponential type, which has presumably not been studied earlier due mainly to their seemingly complicated behavior. We estimate and establish a quantitative asymptotic formula in terms of the modulus of continuity with exponential growth, a Korovkin-type result for exponential functions and also a Voronovskaja-type asymptotic formula in the simultaneous approximation.

scholarly journals INTEGRAL REPRESENTATIONS AND INEQUALITIES OF EXTENDED CENTRAL BINOMIAL COEFFICIENTS

2021 ◽  
Author(s):  
Chunfu Wei
Keyword(s):  
Binomial Coefficient ◽  
Integral Representations ◽  
Binomial Coefficients ◽  
Exponential Functions ◽  
Central Binomial Coefficient

In the paper, the author presents three integral representations of extended central binomial coefficient, proves decreasing and increasing properties of two power-exponential functions involving extended (central) binomial coefficients, derives several double inequalities for bounding extended (central) binomial coefficient, and compares with known results.

scholarly journals A Study on Some New Results Arising from (p,q)-Calculus

2018 ◽  
Author(s):  
Ugur Duran ◽  
Mehmet Acikgoz ◽  
Serkan Araci
Keyword(s):  
Exponential Function ◽  
Chain Rule ◽  
Binomial Coefficients ◽  
Final Part ◽  
Trigonometric Functions ◽  
Elementary Functions ◽  
Exponential Functions ◽  
Hyperbolic Functions ◽  
Quantum Calculus ◽  
A Chain

This paper includes some new investigations and results for post quantum calculus, denoted by (p,q)-calculus. A chain rule for (p,q)-derivative is developed. Also, a new (p,q)-analogue of the exponential function is introduced and some its properties including the addition property for (p,q)-exponential functions are investigated. Several useful results involving (p,q)-binomial coefficients and (p,q)-antiderivative are discovered. At the final part of this paper, (p,q)-analogue of some elementary functions including trigonometric functions and hyperbolic functions are considered and some properties and relations among them are analyzed extensively.

scholarly journals Convergence and Divergence of Higher-Order Hermite or Hermite-Fejér Interpolation Polynomials with Exponential-Type Weights

2012 ◽  
Vol 2012 ◽  
pp. 1-31
Author(s):  
Hee Sun Jung ◽  
Gou Nakamura ◽  
Ryozi Sakai ◽  
Noriaki Suzuki
Keyword(s):  
Exponential Type ◽  
Higher Order ◽  
Divergence Theorem ◽  
Convergence Theorems ◽  
Approximation Process ◽  
Orthonormal Polynomials ◽  
Convergence And Divergence ◽  
Interpolation Polynomials

Let and let , where and is an even function. Then we can construct the orthonormal polynomials of degree for . In this paper for an even integer we investigate the convergence theorems with respect to the higher-order Hermite and Hermite-Fejér interpolation polynomials and related approximation process based at the zeros of . Moreover, for an odd integer , we give a certain divergence theorem with respect to the higher-order Hermite-Fejér interpolation polynomials based at the zeros of .

Some aspects of familiarization with binomial coefficients

2019 ◽  
pp. 49-53
Author(s):  
Abdulkarim Magomedov ◽  
S.A. Lavrenchenko
Keyword(s):  
Elementary Mathematics ◽  
Binomial Coefficients ◽  
Computational Aspects

New laconic proofs of two classical statements of combinatorics are proposed, computational aspects of binomial coefficients are considered, and examples of their application to problems of elementary mathematics are given.

Functions in the Schwartz algebra that are invertible in the sense of Ehrenpreis

2019 ◽  
Vol 484 (1) ◽  
pp. 7-11
Author(s):  
N. F. Abuzyarova
Keyword(s):  
Entire Function ◽  
Exponential Type ◽  
Zero Set ◽  
Schwartz Algebra

We consider the problem of obtaining the restrictions on the zero set of an entire function of exponential type under which this function belongs to the Schwartz algebra and invertible in the sense of Ehrenpreis.

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