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On discrete Picard operators
Author(s) -
Aral Ali,
İnce İlarslan Hatice Gül,
Tunca Gülen Başcanbaz
Publication year - 2016
Publication title -
mathematical methods in the applied sciences
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.719
H-Index - 65
eISSN - 1099-1476
pISSN - 0170-4214
DOI - 10.1002/mma.3894
Subject(s) - mathematics , convergence (economics) , rate of convergence , modulus of continuity , pure mathematics , type (biology) , eulerian path , algebra over a field , mathematical analysis , ecology , channel (broadcasting) , lagrangian , economic growth , electrical engineering , economics , biology , engineering
The present paper is concerned with the approximation properties of discrete version of Picard operators. We first give exact equalities for the moments of the operators. In calculations of these moments, Eulerian numbers play a crucial role. We discuss convergence of these operators in weighted spaces and give Voronovskaya‐type asymptotic formula. The weighted approximation of the operators in quantitative mean in terms of different modulus of continuities is also considered. We emphasize that the rate of convergence of the operators is better than the one obtained in [1][Anastassiou GA, 2013]. Copyright © 2016 John Wiley & Sons, Ltd.