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Starlike functions of complex order involving q-hypergeometric functions with fixed point

Kaliappan VijayaGangadharan MurugusundaramoorthyMurugesan Kasthuri — 2014

Annales Universitatis Paedagogicae Cracoviensis. Studia Mathematica

Recently Kanas and Ronning introduced the classes of starlike and convex functions, which are normalized with ƒ(ξ) = ƒ0(ξ) − 1 = 0, ξ (|ξ| = d) is a fixed point in the open disc U = {z ∈ ℂ: |z| < 1}. In this paper we define a new subclass of starlike functions of complex order based on q-hypergeometric functions and continue to obtain coefficient estimates, extreme points, inclusion properties and neighbourhood results for the function class T Sξ(α, β,γ). Further, we obtain integral means inequalities...

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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