## Abstract

The present note is devoted to a generalization of the notion of shift invariant operators that we call it λ-invariant operators (λ ≥ 0). Some properties of this new class are presented. By using probabilistic methods, three examples are delivered.

## Authors

**Octavian Agratini
**Babes-Bolyai University, Faculty of Mathematics and Computer Science, Ccluj-Napoca, Romania

Tiberiu Popoviciu, Institute of Numerical Analysis, Romanian Academy, Cluj-Napoca, Romanian

## Keywords

### References

see below

## Paper coordinates

O. Agratini, *Shift λ – invariant operators*, Constructive Mathematical Analysis, 2 (2019) 3, 103-108,

doi: 10.33205/cma.544094

## About this paper

##### Journal

Constructive Mathematical Analysis

##### Publisher Name

##### DOI

http://doi/org/10.33205/cma.544094

##### Print ISSN

1651-2939

##### Online ISSN

?

##### Google Scholar Profile

soon

[1] F. Altomare, M. Cappelletti Montano, V. Leonessa, I. Ra¸sa, Markov Operators, Positive Semigroups and Approximation Processes, De Gruyter Studies in Mathematics, Vol. 61, Berlin, 2014.

[2] G. A. Anastassiou, Moments in probability and approximation theory, Pitman Research Notes in Mathematics Series, Vol. 287, Longman Scientific & Technical, England, 1993.

[3] G. A. Anastassiou, S.G. Gal, On some differential shift-invariant integral operators, univariate case revisited, Adv. Nonlinear Var. Inequal., 2(1999), no. 2, 71-83.

[4] G. A. Anastassiou, S.G. Gal, On some differential shift-invariant integral operators, univariate case revisited, Adv. Nonlinear Var. Inequal., 2(1999), no. 2, 97-109.

[5] G. A. Anastassiou, S.G. Gal, On some shift invariant multivariate, integral operators revisited, Commun. Appl. Anal., 5(2001), no. 2, 265-275.

[6] G. A. Anastassiou, H.H. Gonska, On some shift invariant integral operators, univariate case, Annales Polonici Mathematici, LXI(3)(1995), 225-243.

[7] W. Feller, An introduction to probability theory and its applications, Vol. I, II, John Wiley, New York, London, 1957 resp. 1966.

[8] G. G. Lorentz, Approximation of Functions, Holt, Rinehart and Winston, New York, 1966.

[9] D. D. Stancu, Use of probabilistic methods in the theory of uniform approximation of continuous functions, Rev. Roum. Math. Pures et Appl., Tome 14(5)(1969), 673-691.