On sharp bounds of certain Close-to-Convex functions

2019/07/31 by Priyanka Goel, Goel, Priyanka, S. Sivaprasad Kumar +1
Mathematics · #30C45 #30C50 #Analytic and geometric function theory #Complex Variables (math.CV) #FOS: Mathematics #Mathematical Inequalities and Applications

paper · pdf · doi:10.48550/arxiv.1907.13385

openalex publication_date 2019/07/31 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We derive general formula for the fourth coefficient of the functions belonging to the Carathéodory class involving the parameters lying in the open unit disk. Further, we obtain sharp upper bounds of initial inverse coefficients for certain close-to-convex functions satisfying any one of the inequalities: \RE((1-z)f'(z))>0, \RE((1-z²)f'(z))>0, \RE((1-z+z²)f'(z))>0 and \RE((1-z)²f'(z))>0.

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