Differential Inequalities and Univalent Functions

Let ${\mathcal M}$ be the class of analytic functions in the unit disk \ID with the normalization $f(0)=f'(0)-1=0$, and satisfying the condition \left |z^2\left (\frac{z}{f(z)}\right )''+ f'(z)\left(\frac{z}{f(z)} \right)^{2}-1\right |\leq 1, \quad z\in \ID. Functions in $\mathcal{M}$ are known to be univalent in \ID. In this paper, it is shown that the harmonic mean of two functions in ${\mathcal M}$ are closed, that is, it belongs again to ${\mathcal M}$. This result also holds for other related classes of normalized univalent functions. A number of new examples of functions in $\mathcal{M}$ are shown to be starlike in \ID. However we conjecture that functions in $\mathcal{M}$ are not necessarily starlike, as apparently supported by other examples.Comment: 10 pages; To appear in Lobachevskii Journal of Mathematic

The Coefficients Of Functions With Positive Real Part And Some Special Classes Of Univalent Functions.

Several special classes of univalent functions f in the unit disk U are characterized by the quantity zf'(z)/ f (z) lies in a given region in the right-half plane. Amongst these are the classes SS• (a) of strongly starlike functions of order a and PS• (p) consisting of parabolic starlike functions of order p. Both classes are closely related to the class P of nonnalized analytic functions in U with positive real part

Differential Subordination For Meromorphic Functions Defined By A Linear Operator.

By making use of a linear operator that is defined by means of the Hadamard product (or convolution), we investigate the properties of a certain family of meromorphically multivalent functions

Undergraduate Mathematics Enhanced With Graphing Technology.

The School of Mathematical Sciences at University Sains Malaysia has offered a laboratory course on the integration of hand-held technology into the teaching and learning of mathematics since the beginning of the 2001/2002 academic year

Fungsi Analisis Dengan Bahagian Nyata Positif Dan Subkelas Fungsi Univalen.

Beberapa kelas penting fungsi univalen ƒ pada cakera unit U = {z :| z I< I} dapat diterbitkan oleh zƒ(z)/ ƒ(z) supaya terletak di dalam satu rantau yang diberi pada satah sebelah kanan. Di antara kelas tersebut ialah kelas BK(α) yang terdiri daripada fungsi bak-bintang kuat peringkat α dan kelas BP(p) yang mengandungi fungsi bak-bintang parabolik peringkat p. Kedua-d~a kelas ini berkait rapat dengan kelas P yang terdiri daripada fungsi analisis ternormalkan pada U dengan bahagian nyata positif