The interest of the study of almost starlikeness of complex order [lambda] arises from the fact that every almost starlike
mapping f of complex order [lambda] is also spirallike with respect to the operator A = (1 - [lambda])[I.sub.n], and hence f is biholomorphic on [OMEGA] (see ).
Murugusundaramoorthy, "Subclasses of starlike
and convex functions involving Poisson distribution series," Afrika Matematika, vol.
Goodman, "On uniformly starlike
functions," Journal of Mathematical Analysis and Applications, vol.
Since [h.sub.1](z) * [h.sub.2](z) is convex in E, z[hi(z) * [h.sub.2](z)]' is starlike
PONNUSAMY, Coefficient inequalities for concave and meromorphically starlike
univalent functions, Ann.
Also, let (Eq.) and (Eq.) are the classes of strongly starlike
and strongly convex functions of order (Eq.) respectively, that is,
Let [phi] be an analytic and univalent function with positive real part in U with [phi](0) = 1, [phi]'(0) > 0, and [phi] maps the unit disk U onto a region starlike
with respect to 1 and symmetric with respect to the real axis.
Reade, "All a-convex functions are univalent and starlike
," Proceedings of the American Mathematical Society, vol.
The same authors  also obtained the second Hankel determinant and sharp bounds for the familiar subclasses of S, namely, starlike
and convex functions denoted by ST and CV, shown that [absolute value of ([a.sup.2][a.sub.4] - [a.sup.2.sub.3])] [less than or equal to] 1 and [absolute value of ([a.sup.2][a.sub.4] - [a.sup.2.sub.3])] [less than or equal to] 1/8 respectively.
In this paper we investigate the so-called extended eigenvalues and extended eigenvectors and cyclicity problems for some convolution operators acting on the space of analytic functions defined on the starlike
domain D of the complex plane.
The class [S.sup.*.sub.[alpha]] of starlike
functions of order [alpha] < 1 may be defined as
Not long after sunset, the enormous planet appeared as a starlike
brightness by the moon, which was at its fullest.