97 research outputs found
Certain subclasses of multivalent functions defined by new multiplier transformations
In the present paper the new multiplier transformations
\mathrm{{\mathcal{J}% }}_{p}^{\delta }(\lambda ,\mu ,l) (\delta ,l\geq
0,\;\lambda \geq \mu \geq 0;\;p\in \mathrm{% }%\mathbb{N} )} of multivalent
functions is defined. Making use of the operator two new subclasses and \textbf{\ }of multivalent analytic
functions are introduced and investigated in the open unit disk. Some
interesting relations and characteristics such as inclusion relationships,
neighborhoods, partial sums, some applications of fractional calculus and
quasi-convolution properties of functions belonging to each of these subclasses
and
are
investigated. Relevant connections of the definitions and results presented in
this paper with those obtained in several earlier works on the subject are also
pointed out
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
Hadamard Product Concerning Certain Meromorphic Functions
In this paper the authors introduced a new generalized differintegral operator for meromorphic univalent functions in U* = {z : z ∈ C, 0 < |z| < 1}. The objective of this paper is to establish certain results concerning the Hadamard product of functions in the classes ∑^{∗,m}_{μ,λ} (α, β , γ, k) and ∑^h_{μ,λ} (α, β , γ, k)
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