Baskakov - Kantorovich operators reproducing affine functions

Jorge Bustamante


We present a new Kantorovich modification of Baskakov operators which reproduce affine functions. We present an upper estimate for the rate of convergence of the new operators in polynomial weighted spaces and characterized all functions for which there is convergence in the weighted norm.


Baskakov-Kantorovich operators, polynomial weighted spaces, rate of convergence

Full Text:



O. Agratini, {it Kantorovich-type operators preserving affine functions}, Hacet. J. Math. Stat. 45 (6) (2016), 1657-1663.

J. Bustamante, A. Carrillo-Zentella, and J. M. Quesada, {it Direct and strong converse theorems for a general sequence of positive linear operators},

Acta Math. Hungar., 136 (1-2) (2012), 90-106.

J. Bustamante, J. M. Quesada and J. J. Merino, {it

Pointwise estimates for Baskakov operators in weighted

spaces}, to appear

Z. Ditzian and V. Totik, {it Moduli of Smoothness},

Springer, New York (1987).

Guo Feng, {it Direct and inverse approximation theorems for

Baskakov ope-rators with the Jacobi-type weight}, Abstract and Applied Analysis, (2011), Article ID 101852, 13 pages.

A. Holhoc{s}, {it Uniform weighted approximation by positive linear operators}, Stud. Univ. Babes-Bolyai

Math., 56 No. 3, (2011), 135-146.

D.S. Mitrinovi'{c}, J. Peu{c}ari'c and A. M. Fink, {it Classical and New Inequalities in

Analysis}, Kluwer Academic Publishers, Dordrecht, 1993.



  • There are currently no refbacks.