28 research outputs found
Coefficient Conditions for Starlikeness of Nonnegative Order
Sufficient conditions on a sequence {ak} of nonnegative numbers are obtained that ensures f(z)= E°°k=1 akzk is starlike of nonnegative order in the unit disk. A result of Vietoris on trigonometric
sums is extended in this pursuit. Conditions for close to convexity and convexity in the direction
of the imaginary axis are also established. These results are applied to investigate the starlikeness
of functions involving the Gaussian hypergeometric functions
Positive trigonometric sums and applications
Some new positive trigonometric sums that sharpen Vietoris’s classical
inequalities are presented. These sharp inequalities have remarkable applications
in geometric function theory. In particular, we obtain information
for the partial sums of certain analytic functions that correspond to starlike
functions in the unit disk. We also survey some earlier results with additional
remarks and comments
Coefficient Conditions for Starlikeness of Nonnegative Order
Sufficient conditions on a sequence {ak} of nonnegative numbers are obtained that ensures f(z)=∑k=1∞akzk is starlike of nonnegative order in the unit disk. A result of Vietoris on trigonometric sums is extended in this pursuit. Conditions for close to convexity and convexity in the direction of the imaginary axis are also established. These results are applied to investigate the starlikeness of functions involving the Gaussian hypergeometric functions