Properties of Positive Linear Operators Connected with Squared Fundamental Functions

Abstract

The aim of this article is to present a general class of positive linear operators of discrete type related to squared fundamental basis functions. If these operators are expressed by a series, we propose to truncate them by a finite sum while still keeping the property of converging towards the identity operator in a weighted space. A relation between the local smoothness of functions and the local approximation is obtained. In the variant in which the operators are described by a finite sum, we establish the limit of their iterates.

KEYWORDS:

• Contraction principle
• linear positive operator
• Lipschitz function
• modulus of smoothness
• weighted space

2020 MATHEMATICS SUBJECT CLASSIFICATION:

• 41A36
• 47A10

Disclosure statement

No potential conflict of interest was reported by the author.

Additional information

Funding

Not applicable.