On the Generalized Szász–Mirakyan Operators
In this paper, we construct sequences of Szász–Mirakyan operators which are based on a function ρ . This function not only characterizes the operators but also characterizes the Korovkin set 1 , ρ , ρ 2 in a weighted function space. We give theorems about convergence of these operators to the identi...
Saved in:
Published in | Resultate der Mathematik Vol. 65; no. 3-4; pp. 441 - 452 |
---|---|
Main Authors | , , |
Format | Journal Article |
Language | English |
Published |
Basel
Springer Basel
01.06.2014
|
Subjects | |
Online Access | Get full text |
Cover
Loading…
Summary: | In this paper, we construct sequences of Szász–Mirakyan operators which are based on a function
ρ
. This function not only characterizes the operators but also characterizes the Korovkin set
1
,
ρ
,
ρ
2
in a weighted function space. We give theorems about convergence of these operators to the identity operator on weighted spaces which are constructed using the function
ρ
and which are subspaces of the space of continuous functions on
R
+
. We give quantitative type theorems in order to obtain the degree of weighted convergence with the help of a weighted modulus of continuity constructed using the function
ρ
. Further, we prove some shape-preserving properties of the operators such as the
ρ
-convexity and the monotonicity. Our results generalize the corresponding ones for the classical Szász operators. |
---|---|
ISSN: | 1422-6383 1420-9012 |
DOI: | 10.1007/s00025-013-0356-0 |