The present paper deals with notions from the field of complex analysis which have been adapted to fuzzy sets theory, namely, the part dealing with geometric function theory. Several fuzzy differential subordinations are established regarding the operator Lma , given by Lma : An ! An, Lma f (z) = (1 a)Rm f (z) + aSm f (z), where An = f f 2 H(U), f (z) = z + an+1zn+1 + . . . , z 2 Ug is the subclass of normalized holomorphic functions and the operators Rm f (z) and Sm f (z) are Ruscheweyh and S˘al˘agean differential operator, respectively. Using the operator Lma , a certain fuzzy class of analytic functions denoted by SLmF (d, a) is defined in the open unit disc. Interesting results related to this class are obtained using the concept of fuzzy differential subordination. Examples are also given for pointing out applications of the theoretical results contained in the original theorems and corollaries.
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