Approximation with an arbitrary order by modified Baskakov type operators

doi:10.1016/j.amc.2015.05.034

2015-08-01

PRE

Sorin G. Gal *

Bogdan D. Opris

DOI：10.1016/j.amc.2015.05.034

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摘要

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Given an arbitrary sequence lambda(n) > 0, n is an element of N. with the property that lim(n ->infinity) lambda(n) = 0 fast as we want, in this note we consider several kinds of modified Baskakov operators in which the usual knots j/n are replaced with the knots j . lambda(n) . In this way, on each compact subinterval in [0, infinity) the order of uniform approximation becomes omega(1) (f;root lambda(n) ). For example, these modified operators can uniformly approximate a Lipschitz 1 function, on each compact subinterval of [0, infinity) with the arbitrary good order of approximation root lambda(n). Also, similar considerations are made for modified q(n)-Baskakov operators, with 0 < q(n) < 1, lim(n ->infinity) q(n)=1. (C) 2015 Elsevier Inc. All rights reserved.

Keyword:

Modified Baskakov operators

Linear and positive operators

Modulus of continuity

Order of approximation

q-calculus