2022/03/22 by S. Sivaprasad Kumar, Kumar, S. Sivaprasad, Priyanka Goel +1
Mathematics · #Complex Variables (math.CV) #FOS: Mathematics #math.CV
paper · pdf · doi:10.48550/arxiv.2203.11596
arxiv created 2022/03/22 · arxiv updated 2022/03/23
For 0≤α≤ 1, let Hα(x,y) be the convex weighted harmonic mean of x and y. We establish differential subordination implications of the form Hα(p(z),p(z)Θ(z)+zp'(z)Φ(z))\prec h(z)⇒ p(z)\prec h(z), where Φ, Θ are analytic functions and h is a univalent function satisfying some special properties. Further, we prove differential subordination implications involving a combination of three classical means. As an application, we generalize many existing results and obtain sufficient conditions for starlikeness and univalence.