2024/12/30 by Teodor Bulboacă, Bulboacă, Teodor, Milutin Obradović +3
Mathematics · #30C45 #30C50 #Analytic and geometric function theory #Complex Variables (math.CV) #FOS: Mathematics #Mathematical Analysis and Transform Methods #Spectral Theory in Mathematical Physics
paper · pdf · doi:10.48550/arxiv.2412.20857
openalex publication_date 2024/12/30 · openalex created_date 2025/01/01 · openalex updated_date 2026/07/28
In this paper we give simple proofs for the main results concerning generalized Fekete-Szegő functional of type |a3(f)-λa2(f)2|-μ|a2(f)|, where λ∈ℂ, μ>0 and an(f) is n-th coefficient of the power series expansion of f\inS. In addition, we studied this functional separately for the class K of convex functions and we emphasize that all the results of the paper are sharp (i.e. the best possible). The advantages of the present study are that the techniques used in the proofs are more easier and use known results regarding the univalent functions, and those that it give the best possible results not only for the entire class of univalent normalized functions S but also for its subclass of convex functions K.