Analytic functions with conic domains associated with certain generalized q-integral operator

2020/12/26 by Ahuja, Om, Çetinkaya, Asena, Jain, Naveen Kumar
#Complex Variables (math.CV) #FOS: Mathematics

paper · doi:10.48550/arxiv.2012.13776

Abstract

In this paper, we define a new subclass of k-uniformly starlike functions of order γ, (0≤γ<1) by using certain generalized q-integral operator. We explore geometric interpretation of the functions in this class by connecting it with conic domains. We also investigate q-sufficient coefficient condition, q-Fekete-Szegö inequalities, q-Bieberbach-De Branges type coefficient estimates and radius problem for functions in this class. We conclude this paper by introducing an analogous subclass of k-uniformly convex functions of order γ by using the generalized q-integral operator. We omit the results for this new class because they can be directly translated from the corresponding results of our main class.

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