Improved criteria for geometric properties of confluent hypergeometric functions

Abstract

In this paper, we establish sufficient conditions for several geometric properties of confluent hypergeometric functions. Using differential subordination techniques, we derive parameter conditions ensuring lower bounds for the real part of the confluent hypergeometric function and sectorial subordination of its derivative. We also obtain criteria for strong convexity and strong starlikeness of prescribed order. In addition, we investigate the close-to-convexity and starlikeness of the confluent hypergeometric functions. Particular cases yield corresponding results for generalized Laguerre polynomials. The obtained criteria are compared with existing sufficient conditions, and their implications for the geometric theory of special functions are discussed.