Abstract:
Uniformly Convex and Bazilevic Functions
This work is in the field of Geometric Function Theory in which we study geometric
properties of analytic functions. It was originated around the turn of 20th century and has
many applications in the field of applied sciences such as engineering, physics,
electronics, medicines.
In this dissertation, we define and discuss some new subclasses of normalized analytic
functions by using some integral operators such as the operator Q a given by
Q a f(z)
z
a
( )za
1
ta
0
2 log z
t
1
f (t)dt,
where denotes gamma function, f(z) is analytic in open unit disc, a>0 and
0.
We also study generalized Bazilevič functions. The functions in these classes
generalize the idea of Bazilevič functions, k-uniformly convexity and bounded boundary
and bounded radius rotations. The subordination and convolution tools are used to
investigate the geometric properties of the functions in these classes and several inclusion
results with some interesting consequences have been proved. We have investigated the
univalency condition and coefficient bounds, arc length problem, integral preserving
properties and rate of growth of Hankel determinant for these functions. The most of our
results are sharp and they have been connected with previously known results.
