Properties of certain analytic functions associated with two boundary points

Abstract

For analytic functions f (z) in the closed unit disk U, two boundary points z 1 and z 2 such that α = (fThe object of the present paper is to discuss some interesting conditions for f (z) to be |f ′ (z) − 1| < ρ|1 − α| in U with some examples.2010 Mathematics Subject Classification. 30C45.