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 $f(0)=0$ and $f^\prime(0)=1$ in the unit disk $E=\{z\in \mathbb{C}\colon |z|<1\}$. 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 $\alpha>1$, 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 $T_n^\alpha (\beta)$ introduced in \cite{TOO} by Opoola.Comment: 10 pages. Publishe

On H3(1)H_3(1) Hankel determinant for some classes of univalent functions

Focus in this paper is on the Hankel determinant, $H_3(1)$, for the well-known classes of bounded-turning, starlike and convex functions in the open unit disk $E=\{z\in \mathbb{C}\colon|z|<1\}$. The results obtained complete the series of research works in the search for sharp upper bounds on $H_3(1)$ 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 certain analytic functions of bounded boundary rotation

In this paper we introduce certain analytic functions of boundary rotation bounded by $k\pi$ which are of Caratheodory origin. With them we study two classes of analytic and univalent functions in the unit disk $E=\{z\in \mathbb{C}\colon |z|<1\}$, 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 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 nn-starlike integral operators

By a completion of a lemma of Babalola and Opoola \cite{KT}, we prove that certain generalized integral operators preserve $n$-starlikeness in the open unit disk $E=\{z\in \mathbb{C}: |z|<1\}$. 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