Weighted integral transforms involving convolution with some subclasses of analytic functions
Weighted integral transforms involving convolution with some subclasses of analytic functions
Let A represent the class of analytic functions f de
ned in the open unit disk
U := fz 2 C : jzj 0; z 2 U: A functions p analytic in U such that p(0) = 1 belongs
to the class Pk for k 2; if and only if
p (z) =
1
2
Z2
0
1 + ze?i
1 ? ze?i d() (z 2 U) ;
where () : 0 2 is a function of bounded variation satis
es the
conditions
R2
0
d() = 2 and
R2
0 jd()j k: For some 2 R; & 2
and
0; let R
k(
; &) denote the class of functions f 2 A satisfying the
condition:
ei
(1 ?
)
f (z)
z
+
f0 (z) ? &
2 Pk (z 2 U) :
For f 2 R
k(
; &), we de
ne the integral transform=m (f) (z) =
R1
0
m(t) f(tz)
t dt;
where m is a non-negative real-valued weight function with
R1
0
m(t)dt = 1.
The main objective of this paper is to study conditions for invariance of
the integral transforms =m and other relevant properties in connection with
functions in the class R
k(
; &). Also by allowing parameters to vary, we may
encompass a large number of previously known results.
Key words and Phrases: Convolution; Gauss hypergeom
___
- [1] F.S. M.Al Sarari and S. Latha, On symmetrical functions with bounded boundary rotation, J. Math. Comput. Sci., 4(3)(2014), 494-502
- [2] G.E. Andrews, R. Askey, R. Roy, Special functions, Cambridge University Press, Cambridge, 1999
- [3] R. Balasubramanian, S. Ponnusamy and M. Vuorinen, On hypergeometric functions and function spaces, J. Comput. Appl. Math. 139(2)(2002), 299-322.
- ISSN: 2687-6531
- Yayın Aralığı: Yılda 2 Sayı
- Başlangıç: 2019
- Yayıncı: Nihat AKGÜNEŞ
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Weighted integral transforms involving convolution with some subclasses of analytic functions