Nargesi, Mahnaz Moradi
(2013)
Inclusion Properties Of Linear Operators And Analytic Functions.
PhD thesis, Universiti Sains Malaysia.
Abstract
This thesis studies the class A of normalized analytic functions in the open unit
disk U of the complex plane. The class of meromorphic functions in the punctured
unit disk which does not include the origin is also studied. This thesis investigates
six research problems. First, the classical subclasses of starlike, convex, close-toconvex
and quasi-convex functions are extended by introducing new subclasses
of analytic and meromorphic functions. The closure properties of these newly
de ned classes are investigated and it is shown that these classes are closed under
convolution with prestarlike functions and the Bernardi-Libera-Livingston integral
operator.
The univalence of functions f(z) = z +
P1n=2 anzn 2 A is investigated by
requiring the Schwarzian derivative S(f; z) and the second coe cient a2 of f to
satisfy certain inequalities. New criterion for analytic functions to be strongly -
Bazilevi c of nonnegative order is established in terms of the Schwarzian derivatives
and the second coe cients. Also, similar conditions on the second coe cient
of f and its Schwarzian derivative S(f; z) are obtained that would ensure the
function f belongs to particular subclasses of S. For an analytic function f(z) =
z+
P1n
=2 anzn 2 A satisfying the inequality
P1n
=2 n(n
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