There are many results for sufficient conditions of functions f(z) which are analytic in the open unit disc U to be starlike and convex in U. In view of the results due to S. Ozaki, I. Ono and T. Umezawa (1956), P.T. Mocanu (1988), and M. Nunokawa (1993), some sufficient conditions for starlikeness and convexity of f(z) are discussed.
NUNOKAWA, MAMORU; OWA, SHIGEYOSHI; POLATOĞLU, YAŞAR; ÇAĞLAR, MERT; and DUMAN, EMEL YAVUZ
"Some sufficient conditions for starlikeness and convexity,"
Turkish Journal of Mathematics: Vol. 34:
3, Article 4.
Available at: https://journals.tubitak.gov.tr/math/vol34/iss3/4