1,335 research outputs found
Geometric Properties of Partial Sums of Univalent Functions
The th partial sum of an analytic function is the polynomial . A survey of the
univalence and other geometric properties of the th partial sum of univalent
functions as well as other related functions including those of starlike,
convex and close-to-convex functions are presented
A comprehensive class of harmonic functions defined by convolution and its connection with integral transforms and hypergeometric functions
For given two harmonic functions and with real coefficients in
the open unit disk , we study a class of harmonic functions
satisfying \RE \frac{(f*\Phi)(z)}{(f*\Psi)(z)}>\alpha \quad (0\leq
\alpha <1, z \in \mathbb{D}); * being the harmonic convolution. Coefficient
inequalities, growth and covering theorems, as well as closure theorems are
determined. The results obtained extend several known results as special cases.
In addition, we study the class of harmonic functions that satisfy \RE
f(z)/z>\alpha . As an application, their
connection with certain integral transforms and hypergeometric functions is
established.Comment: 14pages, 1 figur
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