Abstract:
In this thesis, certain classes of analytic functions, such as κ − UK η ( λ , α ) ,
i k ( γ , γ , β ) , N
i k ( η , ρ , β ) , R ( m , ρ ) and R λ , p ( a , b , c , A , B ) are
κ − UQC η ( λ , α ) , R
1
2
k
k
introduced. These classes generalize the concepts of uniformly close-to-convex and
quasi-convex, bounded turning, strongly close-to-convex, bounded boundary rotations
and bounded radius rotations. These classes are special generalizations of convex and
related functions. The techniques of convolution and differential subordination are
employed to investigate certain problems such as inclusion results, radius problems, arc
lengths, growth rate of coefficients and Hankel determinant problems and other several
interesting properties of the above mentioned classes. Some well-known results appear as
special cases from our main results.
