524 research outputs found
On certain classes of p-Valent functions by using complex-order and differential subordination.
The aim of the present paper is to study the p-valent analytic functions in the unit disk and satisfy the differential subordinations z(Ip)r, ?(f(z))(j+1)/(p - j)(?p(r, ?)f(z))(j) < (a + (aB + (A- B)ß)z)/a(1 + Bz), where ?p(r, ?) is an operator defined by Salagean and ßis a complex number. Further we define a new related integral operator and also study the Fekete-Szego problem by proving some interesting properties
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
Bounds for the Second Hankel Determinant of Certain Univalent Functions
The estimates for the second Hankel determinant a_2a_4-a_3^2 of analytic
function f(z)=z+a_2 z^2+a_3 z^3+...b for which either zf'(z)/f(z) or
1+zf"(z)/f'(z) is subordinate to certain analytic function are investigated.
The estimates for the Hankel determinant for two other classes are also
obtained. In particular, the estimates for the Hankel determinant of strongly
starlike, parabolic starlike, lemniscate starlike functions are obtained
Subclasses of meromorphically multivalent functions defined by a differential operator
In this paper we introduce and study two new subclasses \Sigma_{\lambda\mu
mp}(\alpha,\beta)\Sigma^{+}_{\lambda\mu mp}(\alpha,\beta)%
(n,\delta)-$neighborhoods of analytic functions to these subclasses of
meromorphically multivalent functions
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
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