Third-order Hankel determinant sharp estimates for the inverse of complex valued holomorphic functions

Muhammad Abbas; Teodor Bulboacă; Reem K Alhefthi; Muhammad Arif

doi:10.1016/j.heliyon.2025.e41666

Third-order Hankel determinant sharp estimates for the inverse of complex valued holomorphic functions

Heliyon. 2025 Jan 8;11(1):e41666. doi: 10.1016/j.heliyon.2025.e41666. eCollection 2025 Jan 15.

Authors

Muhammad Abbas¹, Teodor Bulboacă², Reem K Alhefthi³, Muhammad Arif¹

Affiliations

¹ Department of Mathematics, Abdul Wali Khan University Mardan, Mardan, 23200, Pakistan.
² Research Center of Applied Analysis, Faculty of Mathematics and Computer Science, Babeş-Bolyai University, Cluj-Napoca, 400084, Romania.
³ Department of Mathematics, College of Sciences, King Saud University, P.O. Box 2455, Riyadh, 11451, Saudi Arabia.

Abstract

Determining coefficient estimates of inverse complex valued function is often more challenging than determining the function itself, leading to a lack of articles on inverse functions by examining sharp estimates of the third-order Hankel determinant. This article uses Carathéodory functions to estimate the initial coefficients related to problems for inverse of functions that are bounded turning and subordinated with the cosine function. It covers some inverse coefficients problems together with the second and third-order Hankel determinants. All the estimations that were found are sharp and all the extremal functions and their inverses are also provided.

Keywords: 30C45; 30C50; 30C80; Bounded turning functions; Carathéodory functions; Cosine function; Hankel determinants; Inverse functions.