λ -fractional schwarzian derivative and λ -fractional mobius transformation

Abstract

We denote by A the class of all analytic functions in the open unit disk D=z||z|<1D=z||z|<1 which satisfy the conditions f(0)=0f(0)=0, f′(0)=1f′(0)=1. In this paper we define a new concept of λλ− fractional Schwarzian derivative and λλ− fractional Mobius transformation for the class A. We also formulate the criterion for a function to be univalent using the fractional Schwarzian.