On special fuzzy differential subordinations using Sălăgean and Ruscheweyh operators

In the present paper we establish several fuzzy differential subordinations regarding the operator Lαm, given by Lαm:A→A,Lαmf(z)=(1−α)Rmf(z)+αSmf(z), where Rmf(z) denote the Ruscheweyh derivative, Smf(z) is the Sălăgean operator and An={f∈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 SLFm(δ,α), of analytic functions in the open unit disk 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 SLFm(δ,α). Also, several fuzzy differential subordinations are established regarding the operator Lαm.