Some Classes of Generalized Convex and Related Functions

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.