Abstract
: 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 .
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