New Applications of Sălăgean and Ruscheweyh Operators for Obtaining Fuzzy Differential Subordinations - Alina Alb Lupaş; Georgia Irina Oros (Mathematics, 2021)
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 <semantics><msubsup>Lαm</msubsup></semantics>, given by <semantics><msubsup>Lαm</msubsup>:An→An</semantics>, <semantics><msubsup>Lαm</msubsup>f(z)=(1−α)Rmf(z)+αSmf(z),</semantics> where <semantics>An={f∈H(U),<mspace width="4pt"></mspace>f(z)=z+an+1zn+1+…,<mspace width="4pt"></mspace>z∈U}</semantics> is the subclass of normalized holomorphic functions and the operators <semantics>Rmf(z)</semantics> and <semantics>Smf(z)</semantics> are Ruscheweyh and Sălăgean differential operator, respectively. Using the operator <semantics><msubsup>Lαm</msubsup></semantics>, a certain fuzzy class of analytic functions denoted by <semantics>S<msubsup>LFm</msubsup><mfenced separators="" open="(" close=")">δ,α</mfenced></semantics> 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.