885 research outputs found
Quasi-partial sums of the generalized Bernardi integral of certain analytic functions
In this short note we extend a result of Jahangiri and Farahmand \cite{JM}
concerning functions of bounded turning to a more general class of functions.Comment: Published
Quasi-convolution of analytic functions with applications
In this paper we define a new concept of quasi-convolution for analytic
functions normalized by and in the unit disk . We apply this new approach to study the closure
properties of a certain class of analytic and univalent functions under some
families of (known and new) integral operators.Comment: Published
Bounds on the coefficients of certain analytic and univalent functions
For the real number , we use a technique due to Nehari and
Netanyahu and an application of certain integral iteration of Caratheodory
functions to find the best-possible upper bounds on the coefficients of
functions of the class introduced in \cite{TOO} by Opoola.Comment: 10 pages. Publishe
On certain analytic functions of bounded boundary rotation
In this paper we introduce certain analytic functions of boundary rotation
bounded by which are of Caratheodory origin. With them we study two
classes of analytic and univalent functions in the unit disk , which are also of bounded boundary rotation.Comment: 9 pages. To appear as book chapter in "Inequality Theory and
Application". Eds: S. S. Dragomir and Y. J. Ch
On Hankel determinant for some classes of univalent functions
Focus in this paper is on the Hankel determinant, , for the
well-known classes of bounded-turning, starlike and convex functions in the
open unit disk . The results obtained
complete the series of research works in the search for sharp upper bounds on
for each of these classes.Comment: 7 pages. To appear as book chapter in "Inequality Theory and
Application". Eds: S. S. Dragomir and Y. J. Ch
On some starlike mappings involving certain convolution operators
This paper makes a modest contribution to the family of starlike univalent
mappings in the open unit disk, by the introduction of some new subclasses of
them via certain convolution operators. A new univalence condition is given
with examples. Some basic characterizations of functions of the new subclasses
are also mentioned.Comment: Published
On the successive coefficients of certain univalent functions
The object of this paper is to study relationship between successive
coefficients of some subclasses of the class of univalent functions in the unit
disk. the result obtained is sharp, and is used to provide a new, short proof
of the well-known conjecture of Robertson on the coefficients of
close-to-convex functions.Comment: Publishe
On some -starlike integral operators
By a completion of a lemma of Babalola and Opoola \cite{KT}, we prove that
certain generalized integral operators preserve -starlikeness in the open
unit disk . Our results generalize, extend and
improve many known ones.Comment: 9 pages. Submitte
An invitation to the theory of geometric functions
This note is an invitation to the theory of geometric functions. The
foundation techniques and some of the developments in the field are explained
with the mindset that the audience is principally young researchers wishing to
understand some basics. It begins with the basic terminologies and concepts,
then a mention of some subjects of inquiry in univalent functions theory. Some
of the most basic subfamilies of the family of univalent functions are
mentioned. Main emphasy is on the important class of Caratheodory functions and
their relations with the various classes of functions, especially the
techniques for establishing results in those other classes when compared with
the underlying Caratheodory functions. This is contained in Section 4. Examples
based on this technique are given in the last section. Since the target
audience is the uninitiated, the difficult proofs are not presented. The
elementary proofs are explained in the simplest terms. Footnotes are made to
further explain some not-immediately obvious points. The references are mostly
standard texts. The interested may consult experts for the most recent
references in addition to those contained in the cited texts. Hopefully, this
may as well profit even the initiated who intends to research in this field.Comment: An elementary note on the theory of geometric functions with the
uninitiated in focus. Still under review. Readers' comments are welcom
Some Applications of a Lemma Concerning Analytic Functions Having Positive Real Parts in the Unit Disk
In this paper we give some applications of a lemma of Babalola and Opoola
\cite{BO}, which is a classical extension of an earlier one by Lewandowski,
Miller and Zlotkiewicz \cite{LMZ}. The applications were given via a new
generalization of some well-known subclasses of univalent functions, and they
unify many known results.Comment: 9 pages. Publishe
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