72 research outputs found
Subclasses of Multivalent Meromorphic Functions with a Pole of Order p at the Origin
In this paper, we carry out a systematic study to discover the properties of a subclass of meromorphic starlike functions defined using the Mittag–Leffler three-parameter function. Differential operators involving special functions have been very useful in extracting information about the various properties of functions belonging to geometrically defined function classes. Here, we choose the Prabhakar function (or a three parameter Mittag–Leffler function) for our study, since it has several applications in science and engineering problems. To provide our study with more versatility, we define our class by employing a certain pseudo-starlike type analytic characterization quasi-subordinate to a more general function. We provide the conditions to obtain sufficient conditions for meromorphic starlikeness involving quasi-subordination. Our other main results include the solution to the Fekete–Szegő problem and inclusion relationships for functions belonging to the defined function classes. Several consequences of our main results are pointed out
Convolution, coefficient and radius problems of certain univalent functions [QA331. M231 2009 f rb].
Dengan menggunakan ciri-ciri konvolusi dan teori subordinasi, beberapa subkelas fungsi meromorfi diperkenalkan.
By making use of the properties of convolution and theory of subordination, several subclasses of meromorphic functions are introduced
Subordination And Convolution Of Multivalent Functions And Starlikeness Of Integral Transforms
This thesis deals with analytic functions as well as multivalent functions de-
�ned on the unit disk U. In most cases, these functions are assumed to be normalized,
either of the form
f(z) = z +
1X
k=2
akzk;
or
f(z) = zp +
1X
k=1
ak+pzk+p;
p a �xed positive integer. Let A be the class of functions f with the �rst normalization,
while Ap consists of functions f with the latter normalization. Five
research problems are discussed in this work.
First, let f(q) denote the q-th derivative of a function f 2 Ap. Using the theory
of di�erential subordination, su�cient conditions are obtained for the following
di�erential chain to hold:
f(q)(z)
�(p; q)z
Starlike Functions of Complex Order with Respect to Symmetric Points Defined Using Higher Order Derivatives
In this paper, we introduce and study a new subclass of multivalent functions with respect to symmetric points involving higher order derivatives. In order to unify and extend various well-known results, we have defined the class subordinate to a conic region impacted by Janowski functions. We focused on conic regions when it pertained to applications of our main results. Inclusion results, subordination property and coefficient inequality of the defined class are the main results of this paper. The applications of our results which are extensions of those given in earlier works are presented here as corollaries
Convolution And Coefficient Problems For Multivalent Functions Defined By Subordination
Andaikan C satah kompleks, U = {z E C : Izl < I} cakera unit terbuka dalam
C dan H(U) kelas fungsi analisis dalam U. Andaikan juga A kelas fungsi analisis
1 dalam U yang ternormalkan dengan 1(0) = 0 dan 1'(0) = 1. Fungsi 1 E A
mempunyai siri Taylor berbentuk
00
l(z) = z + L anzn, (z E U).
n=2
Andaikan Ap (p EN) kelas fungsi analisis 1 berbentuk
00
1(z) = zP + L anzn, (z E U)
n=p+1
dengan A := AI.
Pertimbangkan dua fungsi
dalam Ap. Hasil darab Hadamard (atau konvolusi) untuk 1 dan 9 ialah fungsi 1 * 9
berbentuk
00
(J * g)(z) = zP + L anbnzn.
n=p+1
Let C be the complex plane and U := {z E C : Izl < I} be the open unit disk
in C and H(U) be the class of analytic functions defined in U. Also let A denote
the class of all functions I analytic in the open unit disk U := {z E C : Izl < I},
and normalized by 1(0) = 0, and 1'(0) = 1. A function I E A has the Taylor series
expansion of the form
00
I(z) = z + ~ (LnZn (z E U).
n=2
Let Ap (p EN) be the class of all analytic functions of the form
00
fez) = zP + ~ (LnZn
n=p+l
with A:= AI.
Consider two functions
in Ap. The Hadamard product (or convolution) of I and 9 is the function I * 9
defined by
00
(J * g)(z) = zP + ~ anbnzn
.
"=p+
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