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

G. MurugusundaramoorthyK. Uma — 2010

Annales UMCS, Mathematica

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 TSμ/b (α, β, γ) and obtain coefficient estimates, extreme points, the radii of close to convexity, starlikeness and convexity and neighbourhood results for the class TSμ/b (α, β, γ). In particular, we obtain integral means inequalities for the function f(z) belongs to the class TSμ/b (α, β,...

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

G. MurugusundaramoorthyK. Uma — 2010

Annales Universitatis Mariae Curie-Skłodowska, sectio A – Mathematica

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 T S b μ ( α , β , γ ) and obtain coefficient estimates, extreme points, the radii of close to convexity, starlikeness and convexity and neighbourhood results for the class T S b μ ( α , β , γ ) . In particular, we obtain integral means inequalities for the function f ( z ) belongs to the class  T S b μ ( α , β , γ ) in the unit disc.

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