In this paper, we introduce a generalized class of k−uniformly starlike functions and obtain the subordination results and integral means inequalities . Some interesting consequences of our results are also pointed out. 2000 Mathematics Subject Classification: 30C45, 30C80.

We introduce and study a class of starlike functions defined by \begin{equation*} \mathscr{S}^*_\wp:=\left\{f\in\mathcal{A}: \frac{zf'(z)}{f(z)}\prec 1+ze^z=:\wp(z)\right\}, \end{equation*} where $\wp$ maps the unit disk onto cardioid domain. find radius convexity $\wp(z)$ establish inclusion relations between $ \mathscr{S}^*_\wp$ some well-known classes. Further we derive sharp constants coeff...

In this paper, we consider some sufficient conditions for two integral operators to be starlike, close-to-convex and uniformly convex functions defined in the open unit disk. Mathematics subject classification (2000): 30C45.

The objective of the present paper is to give some characterizations for a (Gaussian) hypergeometric function to be in various subclasses of starlike and convex functions. We also consider an integral operator related to the hypergeometric function.

The logarithmic coefficients are very essential in the problems of univalent functions theory. importance is due to fact that bounds on f can transfer Taylor themselves or their powers, via Lebedev–Milin inequalities; therefore, it interesting investigate Hankel determinant whose entries coefficients. main purpose this paper obtain sharp for second strongly starlike and convex functions.

In an earlier paper [l] the writer showed the development of a variational method for starlike functions and applied this method to a general class of extremal problems connected with the coefficients of the function. It is the purpose of this paper to study the classes of extremal problems to which this variational method can be applied and to make some remarks as to its utility. The class S* ...

We investigate harmonic mappings $$f=h+{\bar{g}}$$ defined in the unit disk, where g and h satisfy certain prescribed conditions analytic part belongs to Ma Minda class of starlike functions. Certain sharp radius results for univalency, close-to-convexity, fully starlikeness, convexity, strongly starlikeness are established. also calculate uniformly convexity these Several enhance well-known re...

This is an introductory survey on applications of the Julia variation to problems in geometric function theory. A short exposition is given which develops a method for treating extremal problems over classes F of analytic functions on the unit disk D for which appropriate subsets Fn can be constructed so that (i) F = ⋃ n Fn and (ii) for each f ∈ Fn a geometric constraint will hold that ∂f(D) wi...

Some classes of uniformly starlike and convex functions are introduced. The geometrical properties of these classes and their behavior under certain integral operators are investigated. 1. Introduction. Let A denote the class of functions of the form f (z) = z+ ∞ n=2 a n z