On the improvement of Mocanu's conditions - Nunokawa, M.; Owa, Shigeyoshi; Cho, N. E.; Sokół, J.; Yavuz Duman, Emel (Springer International Publishing, 2013)
We estimate |Arg{p(z)}| for functions of the form p(z)=1+a1z+a2z2+a3z3+⋯ in the unit disc D={z:|z|<1} under several assumptions. By using Nunokawa’s lemma, we improve a few of Mocanu’s results obtained by differential subordinations. Some applications for strongly starlikeness and convexity are formulated.
Keywords: Nunokawa’s lemma; strongly starlike functions of order alpha; strongly convex functions of order alpha; subordination