Inclusion relations and convolution properties of a certain class of analytic functions associated with the Ruscheweyh derivatives

• Published in: Journal of mathematical analysis and applications Vol. 331; no. 1; pp. 686 - 700
• Main Authors: Srivastava, H.M., Xu, N-Eng, Yang, Ding-Gong
• Format: Journal Article
• Language: English
• Published: San Diego, CA Elsevier Inc 01-07-2007; Elsevier
• Subjects: Analytic functions; Close-to-convex functions; Convex functions; Exact sciences and technology; Functions of a complex variable; Hadamard product (or convolution); Mathematical analysis; Mathematics; Ruscheweyh derivatives; Sciences and techniques of general use; Subordination between analytic functions; Univalent functions; Subordination between analytic functions; Hadamard product (or convolution); Analytic functions; Univalent functions; Ruscheweyh derivatives; Convex functions; Close-to-convex functions; Inclusion; Characteristic; Hadamard product; Convolution; Mathematical analysis; Characteristics; Derivative; Convex function; Application; Disk; Analytical function
• ISSN: 0022-247X; 1096-0813
• DOI: 10.1016/j.jmaa.2006.09.019

Let
A
denote the class of functions
f
(
z
)
with
f
(
0
)
=
f
′
(
0
)
−
1
=
0
,
which are analytic in the open unit disk
U
. By means of the Ruscheweyh derivatives, we introduce and investigate the various properties and characteristics of a certain two-parameter subclass
T
(
α
,
λ
;
h
)
of
A
, where
α
≧
0
,
λ
>
−
1
, and
h
(
z
)
is analytic and convex univalent in
U
with
h
(
0
)
=
1
. In particular, some inclusion relations and convolution properties for the function class
T
(
α
,
λ
;
h
)
are presented here.