Let A represent the class of analytic functions f de ned in the open unit disk
U := fz 2 C : jzj < 1g such that f(0) = f0(0) 1 = 0 and let P represent
the well-known class of Carathéodory functions p such that p(0) = 1 and
Re p(z) > 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 + zei
1 zei 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; & < 1; k 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
Hussain Bukhari, S. Z., Razzaq, R., & Ahmed, I. (2021). Weighted integral transforms involving convolution with some subclasses of analytic functions. Ikonion Journal of Mathematics, 3(1), 35-45.
AMA
Hussain Bukhari SZ, Razzaq R, Ahmed I. Weighted integral transforms involving convolution with some subclasses of analytic functions. ikjm. June 2021;3(1):35-45.
Chicago
Hussain Bukhari, Syed Zakar, Rehana Razzaq, and Imtiaz Ahmed. “Weighted Integral Transforms Involving Convolution With Some Subclasses of Analytic Functions”. Ikonion Journal of Mathematics 3, no. 1 (June 2021): 35-45.
EndNote
Hussain Bukhari SZ, Razzaq R, Ahmed I (June 1, 2021) Weighted integral transforms involving convolution with some subclasses of analytic functions. Ikonion Journal of Mathematics 3 1 35–45.
IEEE
S. Z. Hussain Bukhari, R. Razzaq, and I. Ahmed, “Weighted integral transforms involving convolution with some subclasses of analytic functions”, ikjm, vol. 3, no. 1, pp. 35–45, 2021.
ISNAD
Hussain Bukhari, Syed Zakar et al. “Weighted Integral Transforms Involving Convolution With Some Subclasses of Analytic Functions”. Ikonion Journal of Mathematics 3/1 (June 2021), 35-45.
JAMA
Hussain Bukhari SZ, Razzaq R, Ahmed I. Weighted integral transforms involving convolution with some subclasses of analytic functions. ikjm. 2021;3:35–45.
MLA
Hussain Bukhari, Syed Zakar et al. “Weighted Integral Transforms Involving Convolution With Some Subclasses of Analytic Functions”. Ikonion Journal of Mathematics, vol. 3, no. 1, 2021, pp. 35-45.
Vancouver
Hussain Bukhari SZ, Razzaq R, Ahmed I. Weighted integral transforms involving convolution with some subclasses of analytic functions. ikjm. 2021;3(1):35-4.