2025/05/25 by Raju Biswas, Biswas, Raju
Mathematics · #30C45 #30C50 #30C80 #31A05 #Algebraic and Geometric Analysis #Analytic and geometric function theory #Complex Variables (math.CV) #Differential Equations and Boundary Problems #FOS: Mathematics
paper · pdf · doi:10.48550/arxiv.2505.19160
openalex publication_date 2025/05/25 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Let H be the class of harmonic functions f=h+g in the unit disk \mathbbD:=\z∈ℂ:|z|<1\, where h and g are analytic in \mathbbD with the normalization h(0)=g(0)=h'(0)-1=0. Let DH0(α, M) denote the class of functions f=h+ g\inH satisfying the conditions |(1-α)h'(z)+αzh''(z)-1+α|≤ M+|(1-α)g'(z)+αzg''(z)| with g'(0)=0 for z∈\mathbbD, M>0 and α∈(0,1]. In this paper, we investigate fundamental properties for functions in the class DH0(α, M), such as the coefficient bounds, growth estimates, starlikeness and some other properties. Furthermore, we obtain the sharp bound of the second Hankel determinant of inverse logarithmic coefficients for normalized analytic univalent functions f\inP(M) in \mathbbD satisfying the condition Re(zf''(z))>-M for 0