Abstract
Here in this paper, we are using the concepts of
q
-calculus operator theory associated with harmonic functions and define the
q
-Noor integral operator for harmonic functions
f
∈
H
0
.
We investigate a new class
S
H
0
m
,
q
,
α
of harmonic functions
f
∈
H
0
. In this class, we prove a necessary and sufficient convolution condition for the functions
f
∈
H
0
and also we proved that this sufficient coefficient condition is sense preserving and univalent in the class
S
H
0
m
,
q
,
α
. It is proved that this coefficient condition is necessary for the functions in its subclass
T
S
H
0
m
,
q
,
α
. By using this necessary and sufficient coefficient condition, we obtained results based on the convexity and compactness and results on the radii of
q
-starlikeness and
q
-convexity of order
α
in the class
T
S
H
0
m
,
q
,
α
. Also we obtained extreme points for the functions in the class
T
S
H
0
m
,
q
,
α
.