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

Abstract

Let Υ denote the class of functions 𝜒(𝜉) of the form 𝜒(𝜉) = 𝜉 + ∑ 𝑎𝑛∞𝑛=2 𝜉𝑛 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.

Keywords

• analytic function
• quasi-convex
• close to convex
• close to star
• janowski function
• coefficient estimates
• carlson-shaffer operator