Asymptotic formulae for modified Bernstein operators based on regular summability methods

被引：0

作者：

Alemdar, Meryem Ece ^{[1
]}

Duman, Oktay ^{[1
]}

机构：

[1] TOBB Econ & Technol Univ, Dept Math, TR-06530 Sogutozu, Ankara, Turkiye

来源：

HACETTEPE JOURNAL OF MATHEMATICS AND STATISTICS | 2025年 / 54卷 / 03期

关键词：

Bernstein polynomials; Bernstein-Kantorovich polynomials; Voronovskaja-type asymptotic formula; regular summability methods; matrix methods; power series methods; SUMMATION PROCESS; APPROXIMATION; ACCELERATION; CONVERGENCE; RESPECT;

D O I：

10.15672/hujms.1486862

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

In this paper, we get new Voronovskaja-type asymptotic formulae for modified Bernstein operators by using regular summability methods. We also display some significant special cases of our results including the methods of Ces & agrave;ro summability, Riesz summability, Abel summability and Borel summability. At the end, we also discuss the similar results for the Kantorovich version of the operators.

引用

页码：958 / 971

页数：14

共 22 条

[11]

Hardy GH., 1949, Divergent Series

[12]

Kantorovich L. V., 1930, C R ACAD URSS, P563

[13] ACCELERATION BY SUBSEQUENCE TRANSFORMATIONS [J].

KEAGY, TA ;

FORD, WF .

PACIFIC JOURNAL OF MATHEMATICS, 1988, 132 (02) :357-362

[14]

Lorentz G. G., 1953, Mathematical Expositions, V8

[15] QUANTITATIVE RESULTS ON ALMOST CONVERGENCE OF A SEQUENCE OF POSITIVE LINEAR-OPERATORS [J].

MOHAPATRA, RN .

JOURNAL OF APPROXIMATION THEORY, 1977, 20 (03) :239-250

[16]

Phillips G. M., 1997, ANN NUMER MATH, V4, P511, DOI DOI 10.1007/0-387-21682-0_7

[17] Strong summation process in Lp spaces [J].

Sakaoglu, Ilknur ;

Orhan, Cihan .

NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS, 2013, 86 :89-94

[18] ACCELERATION OF LINEAR AND LOGARITHMIC CONVERGENCE [J].

SMITH, DA ;

FORD, WF .

SIAM JOURNAL ON NUMERICAL ANALYSIS, 1979, 16 (02) :223-240

[19] Approximation by positive linear operators in modular spaces by power series method [J].

Tas, E. ;

Yurdakadim, T. .

POSITIVITY, 2017, 21 (04) :1293-1306

[20] Statistical Convergence with Respect to Power Series Methods and Applications to Approximation Theory [J].

Unver, Mehmet ;

Orhan, Cihan .

NUMERICAL FUNCTIONAL ANALYSIS AND OPTIMIZATION, 2019, 40 (05) :535-547

← 1 2 3 →