For real numbers a,q≥0 and a weight ϱ(x)=1/(1+x)q, the author provides necessary and sufficient conditions for a function f∈C[0,∞) in order to supx≥0∣ϱ(x)(Ban(f,x)−f(x))∣→0 as n→∞, where Ban(f) is the Mihesan operator. In particular, it is proved that Mihesan operators behave similar to the classical Baskakov operators.
Citation: |
[1] |
P. N. Agrawal, Th. A. K. Sinha and and A. Sharma, Convergence of derivative of Szász type operators involving Charlier polynomials, Math. Found. Computing, 5 (2022), 1-15.
doi: 10.3934/mfc.2021016.![]() ![]() |
[2] |
M. Becker, Global approximation theorems for Szász-Mirakjan and Baskakov operators in polynomial weight spaces, Indiana Univ. Math. J., 27 (1978), 127-142.
doi: 10.1512/iumj.1978.27.27011.![]() ![]() ![]() |
[3] |
J. Bustamante, A. Carrillo-Zentella and J. M. Quesada, Direct and strong converse theorems for a sequence of positive linear operators, Acta Math. Hungar., 136 (2012), 90-106.
doi: 10.1007/s10474-012-0196-5.![]() ![]() ![]() |
[4] |
J. Bustamante, J. J. Merino-García and J. M. Quesada, Baskakov operators and Jacobi weights: Pointwise estimates, Journal of Inequalities and Applications, (2021), Paper No. 119, 17 pp.
doi: 10.1186/s13660-021-02653-4.![]() ![]() ![]() |
[5] |
I. Gadjev, Weighted approximation by Baskakov operators, Math. Ineq. Appli., 18 (2015), 1443-1461.
doi: 10.7153/mia-18-112.![]() ![]() ![]() |
[6] |
A. Holhoş, Uniform approximation by positive linear operators on noncompact intervals, Automat. Comput. Appl. Math., 18 (2009), 121-131.
![]() ![]() |
[7] |
A. Holhoş, Uniform weighted approximation by positive linear operators, Stud. Univ. Babes-Bolyai Math, 56 (2011), 135-146.
![]() ![]() |
[8] |
V. Mihesan, Uniform approximation with positive linear operators generated by generalized Baskakov method, Autmat. Comput. Appl. Math., 7 (1998), 38-97.
![]() ![]() |
[9] |
A. Wafi and S. Khatoon, Direct and inverse theorems for generalized Baskakov operators in polynomial weight spaces, An. Ştiinţ. Univ. Al. I. Cuza Iaşi. Mat. (N.S.), 50 (2004), 159-173.
![]() |
[10] |
A. Wafi and S. Khatoon, On the order of approximation of functions by generalized Baskakov operators, Indian J. Pure Appl. Math., 35 (2004), 347-358.
![]() ![]() |
[11] |
A. Wafi and S. Khatoon, Convergence and Voronovskaja-type theorems for derivatives of generalized Baskakov operators, Cent. Eur. J. Math., 6 (2008), 325-334.
doi: 10.2478/s11533-008-0025-9.![]() ![]() ![]() |