On Special Fuzzy Differential Subordinations Using Generalized Sala gean Operator and Ruscheweyh Derivative - Alina Alb Lupas (Journal of Advances in Applied & Computational Mathematics, 2017)
: In the present paper we establish several fuzzy differential subordinations regardind the operator RD!," m , given by RD!," m : A # A, RD!," m f (z) = (1#")Rm f (z)+"D! m f (z), where Rm f (z) denote the Ruscheweyh derivative, D! m f (z) is the generalized S ! a l ! a gean operator and A = f !H(U), f (z) = z + a2z 2 +…, z !U is the class of normalized analytic functions. A certain fuzzy class, denoted by RDm F (!,",# ), 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 RDm F (!,",# ). Also, several fuzzy differential subordinations are established regarding the operator RD!," m .