# Approximation of some classes of functions by Landau type operators

## Abstract

This paper aims to highlight a class of integral linear and positive operators of Landau type which have affine functions as fixed points. We focus to reveal approximation properties both in $$L_p$$ spaces and in weighted $$L_p$$ spaces (1≤p<∞). Also, we give an extension of the operators to approximate real-valued vector functions. In this case, the study pursues the approximation of continuous functions on convex compacts. The evaluation of the rate of convergence in one and multidimensional cases is performed by using adequate moduli of smoothness.

## Authors

Octavian Agratini
Faculty of Mathematics and Computer Science, Babeş-Bolyai University, Romania
Tiberiu Popoviciu Institute of Numerical Analysis, Romanian Academy, Romania

Ali Aral
Kirikkale University, Turkey

## Keywords

Landau operator; weighted space; Korovkin theorem, modulus of smoothness

## PDF

Scanned paper.

Latex version of the paper.

## Cite this paper as:

O. Agratini, A. Aral, Approximation of some classes of functions by Landau type operators, Results in Mathematics, 76 (2021) art. no. 12, https://doi.org/10.1007/s00025-020-01319-9

##### Journal

Results in Mathematics

Springer

1422-6383

1420-9012