From uniform to statistical convergence of binomial-type operators

Octavian Agratini
(proceedings), Approximation Theory, paper

Abstract

Sequences of binomial operators introduced by using umbral calculus are investigated from the point of view of statistical convergence. This approach is based on a detailed presentation of delta operators and their associated basic polynomials. Bernstein–Sheffer linear positive operators are analyzed, and some particular cases are highlighted: Cheney–Sharma operators, Stancu operators, Lupaş operators.

Authors

O. Agratini
(Babes-Bolyai University, Cluj-Napoca
Tiberiu Popoviciu Institute of Numerical Analysis, Romanian Academy)

Keywords

Statistical convergence; Binomial sequence; Linear positive operator; Umbral calculus Bernstein–Sheffer operator; Pincherle derivative 

References

See the expanding block below.

Paper coordinates

O. Agratini, From uniform to statistical convergence of binomial-type operators, In: Advances In Summability And Approximation Theory, 169 – 179, (Eds. S. A. Mohiuddine, T. Acar), Springer, Singapore, 2018. ISBN: 978-981-13-3076-6, DOI https://doi.org/10.1007/978-981-13-3077-3_10

PDF

http://ictp.acad.ro/wp-content/uploads/2023/03/2018d-Agratini-From-uniform-to-statistical-convergence-of-binomial-type-operators.pdf

About this paper

Journal
Publisher Name

Springer

DOI

doi.org/10.1007/978-981-13-3077-3_10

Print ISSN

?

Online ISSN

aici se va trece ISSN-ul online

Google Scholar Profile

soon

[1] O. Agratini, On a certain class of approximation operators. Pure Math. Appl. 11(2), 119–127 (2000)MathSciNetzbMATHGoogle Scholar
[2] H. Albayrak, S. Pehlivan, Statistical convergence and statistical continuity on locally solid Riesz spaces. Topol. Appl. 159, 1887–1893 (2012)MathSciNetCrossRefGoogle Scholar
[3] E.W. Cheney, A. Sharma, On a generalization of Bernstein polynomials. Rivista di Matematica Della Università di Parma 5(2), 77–84 (1964)MathSciNetzbMATHGoogle Scholar
[4] H. Fast, Sur le convergence statistique. Colloq. Math. 2, 241–244 (1951)MathSciNetCrossRefGoogle Scholar
[5] A.D. Gadjiev, C. Orhan, Some approximation theorems via statistical convergence. Rocky Mt. J. Math. 32, 129–138 (2002)MathSciNetCrossRefGoogle Scholar
[6] C. Jordan, Calculus of Finite Differences (Chelsea Publishing Company, New York, 1950)zbMATHGoogle Scholar
[7] A. Lupaş, Approximation operators of binomial type, New Developments in Approximation Theory (Dortmund, 1980). International Series of Numerical Mathematics, vol. 132 (Birkhäuser Verlag, Basel, 1999), pp. 175–198CrossRefGoogle Scholar
[8] T. Popoviciu, Remarques sur les polynômes binomiaux. Bulletin de la Société des Sciences de Cluj. Roumanie 6, 146–148 (1931) (also reproduced in Mathematica (Cluj) 6, 8–10 (1932))Google Scholar
[9] G.-C. Rota, D. Kahaner, A. Odlyzko, On the foundations of combinatorial theory, VIII. Finite operator calculus. J. Math. Anal. Appl. 42, 685–760 (1973)MathSciNetCrossRefGoogle Scholar
[10] P. Sablonnière, Positive Bernstein-Sheffer operators. J. Approx. Theory 83, 330–341 (1995)MathSciNetCrossRefGoogle Scholar
[11] D.D. Stancu, Approximation of functions by a new class of linear polynomial operators. Revue Roumaine des Mathématique Pures et Appliquées 13(8), 1173–1194 (1968)MathSciNetzbMATHGoogle Scholar
[12] D.D. Stancu, M.R. Occorsion, On approximation by binomial operators of Tiberiu Popoviciu type. Revue d’Analyse Numérique et de Théorie de l’Approximation 27(1), 167–181 (1998)MathSciNetzbMATHGoogle Scholar
[13] H. Steinhaus, Sur la convergence ordinaire et la convergence asymptotique. Colloq. Math. 2, 73–74 (1951)CrossRefGoogle Scholar

Related Posts