Exploring Fourth-Order Hankel Determinants for Subclasses of Analytic Function using the Lune Function

Abstract

In this paper, the aim was to investigate the Hankel fourth order determinants for the function like Convex and Starlike which was in the form of  and  respectively associated with the Lune operator. The basic goals of this paper were to investigate sharp coefficient bounds for convex and starlike function having normalized form  and  of the function  We derived several inequalities for the coefficients  and  of functions in these classes using a differential subordination method, as well as some known results on Hankel’s determinant. Some existing results in the literature had been expanded and improved by our results. In order to demonstrate the clarity of our results, we provided some examples. The paper will be contributed to the theory and application of univalent functions in comprehensive analysis and geometry.