On Special Fuzzy Differential Subordinations Using Generalized Sala gean Operator and Ruscheweyh Derivative

Abstract

: In the present paper we establish several fuzzy differential subordinations regardind the operator RD!,"m , givenby 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 thegeneralized S !a l!a gean operator and A = { f !H(U), f (z) = z + a2z2 +…, z !U} is the class of normalized analyticfunctions. A certain fuzzy class, denoted by RDmF (!,",# ), of analytic functions in the open unit disc is introduced bymeans of this operator. By making use of the concept of fuzzy differential subordination we will derive various properties and characteristics of the class RDmF (!,",# ). Also, several fuzzy differential subordinations are established regardingthe operator RD!,"m .