A new approximation operator of the Arato-Renyi type

A. Jakimovski, B. Levikson

Research output: Contribution to journalArticlepeer-review


In this paper a new approximation operator is introduced and its properties are studied. Special cases of this operator are the well-known Szàsz power-series approximation operator and its generalization by D. Leviatan. The behaviour of the new approximation operator at points of continuity and discontinuity is investigated by using probabilistic tools as the Chebishev inequality and Liapounov's central limit theorem. Such probabilistic methods of proof simplify the proofs and give better understanding of the approximation mechanism.

Original languageEnglish
Pages (from-to)39-52
Number of pages14
JournalIsrael Journal of Mathematics
Issue number1
StatePublished - Mar 1976
Externally publishedYes

ASJC Scopus subject areas

  • General Mathematics


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