Certain subclasses of starlike functions of complex order involving the Hurwitz-Lerch Zeta function

G. Murugusundaramoorthy ; K. Uma

Annales Universitatis Mariae Curie-Skłodowska, sectio A – Mathematica, Tome 54 (2010), / Harvested from The Polish Digital Mathematics Library

Résumé

Making use of the Hurwitz-Lerch Zeta function, we define a new subclass of uniformly convex functions and a corresponding subclass of starlike functions with negative coefficients of complex order denoted by $TS^\mu _b(\alpha , \beta , \gamma )$ and obtain coefficient estimates, extreme points, the radii of close to convexity, starlikeness and convexity and neighbourhood results for the class $TS^\mu _b(\alpha , \beta , \gamma )$. In particular, we obtain integral means inequalities for the function $f(z)$ belongs to the class $TS^\mu _b(\alpha , \beta , \gamma )$ in the unit disc.

Détail

Publié le : 2010-01-01
EUDML-ID : urn:eudml:doc:289741

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