[1] F.Altomare,M.CappellettiMontano,V.Leonessa,I.Ras ̧a,MarkovOperators,PositiveSemigroupsandApproximation 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. Non- linear 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. Non- linear 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 Mathe- matici, 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.
The present note is devoted to a generalization of the notion of shift invariant operators that we call it $\lambda $-invariant operators $(\lambda \ge 0)$. Some properties of this new class are presented. By using probabilistic methods, three examples are delivered.
[1] F.Altomare,M.CappellettiMontano,V.Leonessa,I.Ras ̧a,MarkovOperators,PositiveSemigroupsandApproximation 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. Non- linear 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. Non- linear 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 Mathe- matici, 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.