Applications of Fuzzy Differential Subordination for a New Subclass of Analytic Functions

This work is concerned with the branch of complex analysis known as geometric function theory, which has been modified for use in the study of fuzzy sets. We develop a novel operator La,?m:An & RARR;An in the open unit disc & UDelta; using the Noor integral operator and the generalized Salagean differential operator. First, we develop fuzzy differential subordination for the operator La,?m and then, taking into account this operator, we define a particular fuzzy class of analytic functions in the open unit disc & UDelta;, represented by R??(m,a,d). Using the idea of fuzzy differential subordination, several new results are discovered that are relevant to this class. The fundamental theorems and corollaries are presented, and then examples are provided to illustrate their practical use.

Automated summary

This work focuses on the application of geometric function theory, a branch of complex analysis, to the study of fuzzy sets. A novel operator La,?m:An & RARR;An is developed in the open unit disc & UDelta; using the Noor integral operator and the generalized Salagean differential operator. The fuzzy differential subordination for La,?m is developed, and a particular class of fuzzy analytic functions in & UDelta; is defined. Several new results relevant to this class are discovered through the concept of fuzzy differential subordination. Fundamental theorems, corollaries, and practical examples are presented.