129 research outputs found
Coefficient and Fekete-Szeg\"o problem estimates for certain subclass of analytic and bi-univalent functions
In this paper, we obtain the Fekete-Szeg\"{o} problem for the -th
root transform of the analytic and normalized functions
satisfying the condition \begin{equation*} 1+\frac{\alpha-\pi}{2 \sin \alpha}<
{\rm Re}\left\{\frac{zf'(z)}{f(z)}\right\} < 1+\frac{\alpha}{2\sin \alpha}
\quad (|z|<1), \end{equation*} where . Afterwards, by the
above two-sided inequality we introduce and investigate a certain subclass of
analytic and bi-univalent functions in the disk and obtain upper bounds
for the first few coefficients and Fekete-Szeg\"{o} problem for functions
belonging to this analytic and bi-univalent function class.Comment: 9 page
Second Hankel Determinant for certain class of bi-univalent functions defined by Chebyshev polynomials
Making use of Chebyshev polynomials, we obtain upper bound estimate for the
second Hankel determinant of a subclass of bi-univalent function class Comment: 13 page
Sub classes of Bi-Univalent Functions Defined by Salagean type Difference Operator
In this paper, we introduce and investigate a new subclass of the function
class of bi-univalent functions defined in the open unit disk, which
are associated with the S\u{a}l\u{a}gean type difference operator and
satisfy some subordination conditions. Furthermore, we find estimates on the
Taylor-Maclaurin coefficients and for functions in the new
subclass introduced here. Several (known or new) consequences of the results
are also pointed out. Further we obtain Fekete-Szeg inequality for
the new function class.Comment: 1
Fekete-Szeg\"o problem for certain classes of Ma-Minda bi-univalent functions
In the present work, we propose to investigate the Fekete-Szeg\"o
inequalities certain classes of analytic and bi-univalent functions defined by
subordination. The results in the bounds of the third coefficient which improve
many known results concerning different classes of bi-univalent functions. Some
interesting applications of the results presented here are also discussed.Comment: 8 Page
Initial coefficient bounds for a general class of bi-univalent functions
Inspired by the recent works of Srivastava et al. (HMS-AKM-PG), Frasin and
Aouf (BAF-MKA) and others
(Ali-Ravi-Ma-Mina-class,Caglar-Orhan,Goyal-Goswami,Xu-HMS-AML,Xu-HMS-AMC), we
propose to investigate the coefficient estimates for a general class of
analytic and bi-univalent functions. Also, we obtain estimates on the
coefficients |a2| and |a3| for functions in this new class. Some interesting
remarks, corollaries and applications of the results presented here are also
discussed.Comment: 8 pages, submitted to a journal for publicatio
Faber polynomial coefficient estimates for a class of analytic bi-univalent functions
In the present paper, we were mainly concerned with obtaining estimates for
the general Taylor-Maclaurin coefficients for functions in a certain general
subclass of analytic bi-univalent functions. For this purpose, we used the
Faber polynomial expansions. Several connections to some of the earlier known
results are also pointed out.Comment: arXiv admin note: text overlap with arXiv:1808.06514 by other author
On quasi subordination for analytic and biunivalent function class
In this work, the subclass of the function class S of bi-univalent functions
associated with the quasi-subordination is defined and studied. Also some
relevant classes are recognized and connections to previus results are made.Comment: 12 page
Initial Coefficients of Bi-univalent Functions
An analytic function defined on the open unit disk
is bi-univalent if the function and its inverse
are univalent in . Estimates for the initial coefficients
of bi-univalent functions are investigated when and
respectively belong to some subclasses of univalent functions. Some earlier
results are shown to be special cases of our results
Coefficients of the Inverse Functions and Radius Estimates of Certain Starlike Functions
Ma-Minda class (of starlike functions) consists of all normalized analytic
functions on the unit disk for which the image of is
contained in the some starlike region in the right-half plane. We obtain the
best possible bounds on the second and third coefficient for the inverse
functions of functions in the Ma-Minda class. The bounds on the Fekete-Szeg\"o
functional and the second Hankel determinant of the inverse functions of the
functions belonging to the Ma-Minda class are also determined. Further, the
bounds on the first five coefficients of the inverse functions are investigated
for two particular subclasses of the Ma-Minda class. In addition, some radius
estimates associated with the two subclasses are also computed
Initial coefficient bounds for certain classes of Meromorphic bi-univalent functions
In this paper we extend the concept of bi-univalent to the class of
meromorphic functions. We propose to investigate the coefficient estimates for
two classes of meromorphic bi-univalent functions. Also, we find estimates on
the coefficients |b0| and |b1| for functions in these new classes. Some
interesting remarks and applications of the results presented here are also
discussed.Comment: 7 pages, submitted a journal for publicatio
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