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

Kaliappan Vijaya, Gangadharan Murugusundaramoorthy, Murugesan Kasthuri

Abstract


Recently Kanas and Ronning introduced the classes of starlike and convex functions, which are normalized with f(ξ)=f'(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 TSξ(α , β, γ). Further, we obtain integral means inequalities for the function f∈TSξ(α , β, γ).

Keywords


Univalent, Starlike, Convex, Uniformly convex, Uniformly starlike, Hadamard product, q- Hypergeometric functions, q-shifted factorial, general operator, integral means inequalities, neighborhood

Mathematics Subject Classification (2010)


30C45

References


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