COEFFICIENT BOUNDS FOR CERTAIN SUBCLASSES OF QUASI-CONVEX FUNCTIONS ASSOCIATED WITH CARLSON-SHAFFER OPERATOR

Let Υ denote the class of functions χ(ξ) of the form χ(ξ)=ξ+∑_(n=2)^∞▒a_n ξ^n which are analytic in the open unit disc Δ=\{ 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 the 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.