A note on special fuzzy differential subordinations using generalized Sălăgean operator and Ruscheweyh derivative.

In the present paper we establish several fuzzy differential subordinations regardind the operator RDmλ,α. given by RDmλ,α : An -→ An, RDmλ,α = (l-α)Rmf(z)+αDmλf(z)-. where Rmf(z) denote the Ruscheweyh derivative, RDmλ f(z) is the generalized Sǎlǎgean operator and An = {f ∈013; H(U), f(z) = z+an+1zn+1+..., z ∈ U} is the class of normalized analytic functions with A1 = A, A certain fuzzy class, denoted by RDFm (δ, λ, α). of analytic functions in the open unit disc is introduced by means of this operator. By making use of the concept of fuzzy differential subordination we will derive various properties and characteristics of the class RDFm (δ, λ, α). Also, several fuzzy differential subordinations are established regarding the operator RDmλ,α. [ABSTRACT FROM AUTHOR]