In the present paper, a theorem for the starlikeness and convexity of multivalent functions involving certain inequalities is given. Some interesting consequences of the main result are also mentioned.
The hereditary properties of convexity and starlikeness for conformal mappings do not generalize to univalent harmonic mappings. This failure leads to the notions of fully starlike and fully convex mappings. In this paper, properties of fully starlike mappings of order α and fully convex mappings of order α (0 ≤ α < 1) are studied; in particular, the bounds for the radius of full starlikeness of order α as well as the radius of full convexity of order α are determined for certain families of...
We obtain several fuzzy differential subordinations by using a linear operator . Using the linear operator we also introduce a class of univalent analytic functions for which we give some properties.
∗ Partially supported by grant No. 433/94 NSF of the Ministry of Education and Science of the Republic of Bulgaria 1991 Mathematics Subject Classification:30C45We consider functions of the type, j=1 ... n, F(z) = z^p ∏ [ fj (z)/(z^p) ] ^αj where fj are p-valent functions starlike of order αj and aj are complex numbers. The problem we solve is to find conditions for the centre and the radius of the disc {z : |z − ω| < r}, contained in the unit disc {z : |z| < 1} and containing the origin,...