Fuzzy Differential Subordination Associated with a General Linear Transformation

In this study, we investigate a possible relationship between fuzzy differential subordination and the theory of geometric functions. First, using the Al-Oboudi differential operator and the Babalola convolution operator, we establish the new operator BS alpha,lambda m,t:A(n)-> A(n) in the open unit disc U. The second step is to develop fuzzy differential subordination for the operator BS alpha,lambda m,t. By considering linear transformations of the operator BS alpha,lambda m,t, we define a new fuzzy class of analytic functions in U which we denote by T-F(lambda,t)(m,alpha,delta). Several innovative results are found using the concept of fuzzy differential subordination and the operator BS alpha,lambda m,t for the function f in the class T-F(lambda,t)(m,alpha,delta). In addition, we explore a number of examples and corollaries to illustrate the implications of our key findings. Finally, we highlight several established results to demonstrate the connections between our work and existing studies.