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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.

Coefficient bounds for some subclasses of p-valently starlike functions

C. SelvarajO. S. BabuG. Murugusundaramoorthy — 2013

Annales UMCS, Mathematica

For functions of the form f(z) = zp + ∑∞n=1 ap+n zp+n we obtain sharp bounds for some coefficients functionals in certain subclasses of starlike functions. Certain applications of our main results are also given. In particular, Fekete-Szegö-like inequality for classes of functions defined through extended fractional differintegrals are obtained

Coefficient bounds for some subclasses of p-valently starlike functions

C. SelvarajO. S. BabuG. Murugusundaramoorthy — 2013

Annales Universitatis Mariae Curie-Skłodowska, sectio A – Mathematica

For functions of the form f ( z ) = z p + n = 1 a p + n z p + n we obtain sharp bounds for some coefficients functionals in certain subclasses of starlike functions. Certain applications of our main results are also given. In particular, Fekete-Szego-like inequality for classes of functions defined through extended fractional differintegrals are obtained.

A subclass of harmonic functions with varying arguments defined by Dziok-Srivastava operator

G. MurugusundaramoorthyKaliappan VijayaRavinder Krishna Raina — 2009

Archivum Mathematicum

Making use of the Dziok-Srivastava operator, we introduce a new class of complex valued harmonic functions which are orientation preserving and univalent in the open unit disc and are related to uniformly convex functions. We investigate the coefficient bounds, distortion inequalities and extreme points for this generalized class of functions.

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