COEFFICIENT INEQUALITIES FOR A CERTAIN CLASS OF CLOSE-TO-STAR FUNCTIONS DEFINED BY SUBORDINATION
By
S. Kalaiselvan1, K. Suchithra2 , T. Thulasiram3* and T.V. Sudharsan4
1Department of Mathematics, Guru Nanak College, Chennai, Tamil Nadu, India-600042 2,3Department of Mathematics, A.M. Jain College, Chennai, Tamil Nadu, India - 600061 4Department of Mathematics, S.I.V.E.T. College, Gowrivakkam, Chennai, Tamil Nadu, India - 600073, No.3, Pari street, Chitlapakkam, Chennai, Tamil Nadu, India -600064
Email: kalaiselvan.s@gurunanakcollege.edu.in, suchithra.k@amjaincollege.edu.in, thulasiram.t@amjaincollege.edu.in, tvsudharsan@gmail.com*Corresponding author
(Received: November 03, 2025; In format: November 05, 2025; Revised June 25, 2026; Accepted: June 29, 2026)
DOI: https://doi.org/10.58250/jnanabha.2026.56118
Abstract
A class of close-to-star functions CSφ = {f ∈ A : (1−z) 2 f(z)/z ≺ φ(z)} defined by subordination is presented in this study. For the class CSφ , coefficient estimates, bounds for the second and third order Hermitian Toeplitz determinants, and Fekete-Szeg¨o inequality is established. Further, Hermitian Toeplitz determinants and Fekete-Szeg¨o inequality are discussed for specific cases of φ.
2020 Mathematical Sciences Classification: 30C45, 30C50.
Keywords and Phrases: Analytic functions, Close-to-star functions, Subordination, Hermitian Toeplitz determinants