Abstract:
The core objective of this research is to introduce new classes of analytic functions by
using the concept of bounded boundary rotation and some of its generalization. This
research heavily depends on the recent techniques of convolution (Hadamard product)
and the differential subordination. The Ruscheweyh derivative and Carlson-Shaffer
operator are utilized to define certain new classes of analytic functions. We also
investigate these classes for certain linear operators such as Jung-Kim-Srivastava
operator, generalized Bernardi integral operator, Frasin integral operator and some others.
Some geometrical and analytical properties, which include distortion bounds, radius
problems, inclusion relation, rate of growth problem and integral representation, are
explored systematically. Relevant connections of the results presented here with those
obtained in earlier works are pointed out. This research is updated with the advancement
and changing trends in the field of Geometric Function Theory and emerging new open
problems are added for investigation.
