A new modification of Gamma operators with a better error estimation. (English) Zbl 1514.41019

Usta, Fuat; Betus, Ömür

Linear Multilinear Algebra 70, No. 11, 2198-2209 (2022).

Summary: The present paper deals with new modification of Gamma operators preserving polynomials in Bohman-Korovkin sense and study their approximation properties: Voronovskaya type theorems, weighted approximation and rate of convergence are captured. The effectiveness of the newly modified operators according to classical ones are presented in certain senses as well. Numerical examples are also presented, highlighting the performance of the new constructions of Gamma operators in the context of one dimensional approximation.

MSC:

41A36	Approximation by positive operators
41A25	Rate of convergence, degree of approximation

Keywords:

Gamma operator; Voronovskaya type theorems; weighted approximation; rate of convergence; numerical results

References:

[1]	King, JP., Positive linear operators which preserve \(####\), Acta Math Hung, 99, 203-208 (2003) · Zbl 1027.41028
[2]	Lupaş, A.; Müller, M., Approximations eigenschaften der Gamma operatoren, Math Zeitschr, 98, 208-226 (1967) · Zbl 0171.02301
[3]	Artee, Approximation by modified Gamma type operators, Int J Adv Appl Math Mech, 5, 4, 12-19 (2018) · Zbl 1473.41005
[4]	Karslı, H., Rate of convergence of new Gamma type operators for functions with derivatives of bounded variation, Math Comput Model, 45, 5-6, 617-624 (2007) · Zbl 1165.41316
[5]	Karslı, H., Direct local and global approximation results for operators of gamma type, Hacet J Math Stat, 39, 2, 241-253 (2010) · Zbl 1203.41009
[6]	Rempulska, L.; Skorupka, M., Approximation properties of modified gamma operators, Integral Transform Spec Funct, 18, 9, 653-662 (2007) · Zbl 1148.41025
[7]	Zeng, XM., Approximation properties of gamma operators, J Math Anal Appl, 311, 2, 389-401 (2005) · Zbl 1087.41024
[8]	Gadjiev, AD., Theorems of the type of P. P. Korovkin’s theorems, Mat Zametki, 20, 5, 781-786 (1976) · Zbl 0383.41016