We define new classes of the family E(Φ,Ψ), in a unit disk U := {z ∈ C, |z| < 1}, as follows: for analytic functions F (z),Φ(z) and Ψ(z) so that <{ (z)∗Φ(z) F (z)∗Ψ(z)} > 0, z ∈ U, F (z) ∗Ψ(z) 6= 0 where the operator ∗ denotes the convolution or Hadamard product. Moreover, we establish some subordination results for these new classes.

Abstract In this note, we formulate a new linear operator given by Airy functions of the first type in complex domain. We aim to study view geometric function theory based on subordination and superordination concepts. The is suggested define class normalized (the univalent functions) calling difference formula. As result, formula joining modified different classes analytic open unit disk.

Abstract In the present paper, by using concept of convolution and q -calculus, we define a certain -derivative (or -difference) operator for analytic multivalent p -valent) functions. This presumably new is an extension known -analogue Ruscheweyh derivative operator. We also give some interesting applications this functions method differential subordination. Relevant connections with number ea...

First, we introduce some basic notation which is used in this paper. Throughout the entire paper, the unit disk in the finite complex plane C will be denoted by D. H D will denote the space of all analytic functions on D. Every analytic self-map φ of the unit disk D induces through composition a linear composition operator Cφ fromH D to itself. It is a well-known consequence of Littlewood’s sub...