INTEGRAL OPERATORS AND THEIR EFFECT ON GEOMETRIC PROPERTIES OF UNIVALENT FUNCTIONS
Nidhi,
Research Scholar,
Dr. Vineeta Basotia,
Research Guide,
Department of Mathematics, Shri JJT University, Jhunjhunu, Rajasthan, India
Abstract : In this paper, we investigate the impact of certain integral operators on the geometric properties of univalent functions defined in the open unit disk. By applying these operators to standard subclasses of univalent functions, we examine the preservation and transformation of geometric characteristics such as starlikeness, convexity, and close-to-convexity. Sufficient conditions are established under which the integral operators map functions from one geometric class into another. Several inclusion relationships and sharp bounds are derived to illustrate the effectiveness of the operators. The results generalize and unify a number of earlier works in the theory of geometric function theory and provide new insights into the structural behavior of univalent functions under integral transformations.
Keywords: Univalent functions; integral operators; starlike functions; convex functions; geometric function theory; analytic functions
