Open AccessSimultaneous Approximation by Modification of Classical Szãsz Operators with Parameter s
Author(s) -
Ali Jasem Mohammed,
T. A. Abdul-Qader,
S. A. Abdul-Hammed
Publication year - 2021
Publication title -
journal of physics. conference series
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.21
H-Index - 85
eISSN - 1742-6596
pISSN - 1742-6588
DOI - 10.1088/1742-6596/1879/3/032018
Subject(s) - sequence (biology) , order (exchange) , mathematics , type (biology) , function (biology) , first order , pure mathematics , combinatorics , chemistry , ecology , biochemistry , finance , evolutionary biology , economics , biology
This paper is approving the simultaneous approximation order by a modification family of the classical sequence of Szãsz operators. This modification depends on a real parameter s > −1/2. First, we show that this family (or its derivatives) converges to the function (or the corresponding derivatives) being approximated. Next, a Voronovski-type asymptotic formula for this family is given. The order of this approximation is improved from the order O ( n −1 ) (the order of the classical sequence) to the order O ( n −(2 s +1) ) whenever s > 0. Finally, the study supports by some numerical examples and discusses the results obtained.