The aim of this scientific note is first to present certain information associated with the Tremblay operator in the complex plane and then to determine several results constituted by the related operator for certain analytic functions and also to point some implications of them out. 2010 Mathematics Subject Classification: 26A33, 34A08, 35G10, 35F05, 30C55, 30C45, 30A10 Key words and phrases: complex plane, unit open disk, normalized analytic function, fractional calculus, tremblay operator, equations and inequalities in the complex plane

In this paper we prove a general result regarding the radius of convexity for different particular functions. The method of convolutions is used. The results are applied to deduce sharp bounds regarding functions, which satisfy differential subordinations.