18 research outputs found
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
Applications of Theory of Differential Subordination for Functions with Fixed Initial Coefficient to Univalent Functions
By using the theory of first-order differential subordination for functions
with fixed initial coefficient, several well-known results for subclasses of
univalent functions are improved by restricting the functions to have fixed
second coefficient. The influence of the second coefficient of univalent
functions is evident in the results obtained