2020/11/23 by S. Sivaprasad Kumar, Kumar, S. Sivaprasad, Shagun Banga +1
Mathematics · #Analytic and geometric function theory #Complex Variables (math.CV) #FOS: Mathematics #Holomorphic and Operator Theory #math.CV
paper · pdf · doi:10.48550/arxiv.2011.11404
arxiv created 2020/11/23 · openalex publication_date 2020/11/23 · arxiv updated 2020/11/24 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Let h be a non vanishing convex univalent function and p be an analytic function in \mathbbD. We consider the differential subordination ψi(p(z), z p'(z)) \prec h(z) with the admissible functions in consideration as ψ1:=(βp(z)+γ)-α(\tfrac(βp(z)+γ)β(1-α)+ z p'(z)) and ψ2:=\tfrac1√(γβ)\arctan(√(\tfracβγ)p1-α(z))+(\tfrac1-αβp2 (1-α)(z)+γ)\tfracz p'(z)pα(z). The objective of this paper is to find the dominants, preferably the best dominant(say q) of the solution of the above differential subordination satisfying ψi(q, n zq'(z))= h(z). Further, we show that ψi(q,zq'(z))= h(z) is an exact differential equation and q is a convex univalent function in \mathbbD. In addition, we estimate the sharp lower bound of \RE p for different choices of h and derive a univalence criteria for functions in H(class of analytic normalized functions) as an application to our results.