On the Determinants for a Class of Analytic Function Using Sigmoid Beta-Catas Operator - Olubunmi A. Fadipe-Joseph; Olanike R. Oluwaseyi; E. O. Opaleye; Uzoamaka A. Ezeafulukwe (Journal of Function Spaces)
Geometric function theory (GFT) is the study of geometric properties of analytic functions. The cornerstone of GFT is the theory of univalent functions. Several related topics in GFT with various applications have been developed over the years, one of which includes the study of special functions. In particular, the sigmoid function in relation to GFT is being investigated. However, the connection between the modified sigmoid function and the β - Catas differential operator is yet to be studied. In this paper, a new class of analytic function is defined using the Sigmoid β− Catas operator. The corresponding coefficient bounds, Fekete–Szego functional, and second order and third order Hankel determinants were determined by the principle of subordination. Furthermore, the second order and third order Toeplitz determinants for this class were also obtained.