## 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

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## 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

## About this paper

##### Print ISSN

1422-6383

##### Online ISSN

1420-9012

##### Google Scholar Profile

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