Generalized Close-to-Convex Functions and Related Topics

Abstract

Aim of this thesis is to introduce and study properties of certain new subclasses of analytic functions in the open unit disc. The concepts of q-calculus are used to define the q-extensions of starlike and close-to-convex functions. “q-Bernardi Integral Operator’’ which is the advancement of well-known Bernardi integral operator is investigated. It is shown that our newly defined classes are invariant under this integral operator. Further, Ordinary fractional derivative operator and q-fractional derivative operator are used to study certain interesting properties of these classes. The idea of qbounded radius rotation and the behavior of starlike functions of negative order with negative coefficients involving q-difference operator is also examined. The relevant connections of our new classes and results to known ones are also pointed out.