Some applications of a differential subordination (Q1587827)

A number of interesting criteria were given by (for example) \textit{R. Singh} and \textit{S. Singh} [Proc. Am. Math. Soc. 106, No. 1, 145-152 (1989; Zbl 0672.30007)], \textit{L. Yi} and \textit{S. Ding} [Internat. J. Math. Math. Sci. 19, 613-614 (1996; Zbl 0849.30007)], and \textit{M. Nunokawa} and \textit{D. K. Thomas} [in: Current topics in analytic function theory, World Sci. Publishing Company, Singapore, New Jersey, London, and Hong Kong, 212-219 (1992)], for a normalized analytic function to be in the familiar class \(S^*\) of starlike functions. The main object of the present paper is to extend and improve each of these earlier results. An application associated with an integral operator \(F_c(c> -1)\) is also considered.