New Applications of Fuzzy Set Concept in the Geometric Theory of Analytic Functions

Zadeh’s fuzzy set theory offers a logical, adaptable solution to the challenge of defining, assessing and contrasting various sustainability scenarios. The results presented in this paper use concept embedded into theories differential subordination superordination established developed geometric function theory. As an extension classical subordination, was first introduced 2011. In order generalize idea superordination, dual notion later, 2017. two concepts are applied article making previously operator defined as convolution product generalized Sălgean Ruscheweyh derivative. Using operator, new subclass functions, normalized analytic U, is investigated. It proved that class convex, subordinations by applying known lemmas using functions from aforementioned operator. When possible, best dominants also indicated for subordinations. Furthermore, involving superordinations which subordinants given. Certain corollaries obtained particular convex or theorems numerous examples constructed both prove applicability theoretical study.