TY - JOUR
ID -
TI - On Some Approximation Properties for a Sequence of -Bernstein Type Operators
AU - Ali Jassim Muhammad
AU - Asma Jaber
PY - 2021
VL - 62
IS - 12
SP - 4903
EP - 4915
JO - Iraqi Journal of Science المجلة العراقية للعلوم
SN - 00672904 23121637
AB -
In 2010, Long and Zeng introduced a new generalization of the Bernstein polynomials that depends on a parameter and called -Bernstein polynomials. After that, in 2018, Lain and Zhou studied the uniform convergence for these -polynomials and obtained a Voronovaskaja-type asymptotic formula in ordinary approximation. This paper studies the convergence theorem and gives two Voronovaskaja-type asymptotic formulas of the sequence of -Bernstein polynomials in both ordinary and simultaneous approximations. For this purpose, we discuss the possibility of finding the recurrence relations of the -th order moment for these polynomials and evaluate the values of -Bernstein for the functions , is a non-negative integer.
ER -