Coefficient Bounds For Certain Subclasses Of Quasi-Convex Functions Associated With Carlson-Shaffer Operator

ABSTRACT

Let denote the class of functions χ(ξ) of the form χ(ξ)=ξ+n=2ann which are analytic in the open unit disc  ={ ξ∈C: |ξ|<1 }. In recent times investigating the properties of several existing and new subclasses of quasi-convex functions have gained importance and attracted researchers working in the theory of univalent functions. Using Carlson-Shaffer operator, we introduce new subclasses of quasi-convex functions. The coefficient bounds for functions belonging to the defined function classes are our main results. Further, we establish various well known results as corollaries to our main results.