Fekete-Szegö Inequality Estimate for Analytic Functions Using Salagean-Difference Operator and Leaf-Like Domain

This paper investigates the Fekete-Szego inequality for subclasses of analytic functions in the unit disk, including starlike, convex, bounded turning, and close-to-convex functions of complex order. Employing the Salagean-diference operator, we derive sharp bounds for the functional b₂γ{b₂²} and extend these results to leaf-like domains. Our findings generalize classical inequalities, offering new insights into coefficient constraints and geometric properties in complex analysis.