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

[1] General Summability Methods in the Approximation by Bernstein-Chlodovsky Operators [J].

Alemdar, Meryem Ece ;

Duman, Oktay .

NUMERICAL FUNCTIONAL ANALYSIS AND OPTIMIZATION, 2021, 42 (05) :497-509

[2] Approximation by nonlinear integral operators via summability process [J].

Aslan, Ismail ;

Duman, Oktay .

MATHEMATISCHE NACHRICHTEN, 2020, 293 (03) :430-448

[3] Summation process of positive linear operators [J].

Atlihan, Oe. G. ;

Orhan, C. .

COMPUTERS & MATHEMATICS WITH APPLICATIONS, 2008, 56 (05) :1188-1195

[4]

Bernstein S.N., 1912, Commun Kharkov Math Soc, V12, P1

[5]

Bojanic R., 1983, Proc. of the Canadian Math. Soc, V3, P5

[6]

Boos J., 2000, Classical and modern methods in summability

[7] MATRIX SUMMABILITY OVER CERTAIN CLASSES OF SEQUENCES ORDERED WITH RESPECT TO RATE OF CONVERGENCE [J].

DAWSON, DF .

PACIFIC JOURNAL OF MATHEMATICS, 1968, 24 (01) :51-&

[8] Approximation via Power Series Method in Two-Dimensional Weighted Spaces [J].

Demirci, Kamil ;

Yildiz, Sevda ;

Dirik, Fadime .

BULLETIN OF THE MALAYSIAN MATHEMATICAL SCIENCES SOCIETY, 2020, 43 (06) :3871-3883

[9]

Fejér L, 1904, MATH ANN, V58, P51

[10] Regular summability methods in the approximation by max-min operators [J].

Gokcer, Turkan Yeliz ;

Duman, Oktay .

FUZZY SETS AND SYSTEMS, 2022, 426 :106-120

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