New Applications of S?l?gean and Ruscheweyh Operators for Obtaining Fuzzy Differential Subordinations

Alina Alb Lupaş and Georgia Irina Oros
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Alina Alb Lupaş: Department of Mathematics and Computer Science, University of Oradea, 1 Universitatii Street, 410087 Oradea, Romania
Georgia Irina Oros: Department of Mathematics and Computer Science, University of Oradea, 1 Universitatii Street, 410087 Oradea, Romania

Mathematics, 2021, vol. 9, issue 16, 1-12

Abstract: 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 L ? m , given by L ? m : A n ? A n , L ? m f ( z ) = ( 1 ? ? ) R m f ( z ) + ? S m f ( z ) , where A n = { f ? H ( U ) , f ( z ) = z + a n + 1 z n + 1 + … , z ? U } is the subclass of normalized holomorphic functions and the operators R m f ( z ) and S m f ( z ) are Ruscheweyh and S?l?gean differential operator, respectively. Using the operator L ? m , a certain fuzzy class of analytic functions denoted by S L F m ? , ? 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.

Keywords: fuzzy differential subordination; convex function; fuzzy best dominant; differential operator (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2021
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