On special fuzzy differential subordinations using Sălăgean and Ruscheweyh operators.

In the present paper we establish several fuzzy differential subordinations regarding the operator L α m , given by L α m : A → A , L α m f ( z ) = ( 1 − α ) R m f ( z ) + α S m f ( z ) , where R m f ( z ) denote the Ruscheweyh derivative, S m f ( z ) is the Sălăgean operator and A n = { f ∈ H ( U ) , f ( z ) = z + a n + 1 z n + 1 + ⋯ , z ∈ U } is the class of normalized analytic functions with A 1 = A . A certain fuzzy class, denoted by S L F m ( 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 S L F m ( δ , α ) . Also, several fuzzy differential subordinations are established regarding the operator L α m . [ABSTRACT FROM AUTHOR]