Logarithmic Coefficients Inequality for the Family of Functions Convex in One Direction

Ebrahim Analouei Adegani, Ahmad Motamednezhad, Mostafa Jafari and Teodor Bulboacă ()
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Ebrahim Analouei Adegani: Faculty of Mathematical Sciences, Shahrood University of Technology, Shahrood P.O. Box 316-36155, Iran
Ahmad Motamednezhad: Faculty of Mathematical Sciences, Shahrood University of Technology, Shahrood P.O. Box 316-36155, Iran
Mostafa Jafari: Department of Mathematics, Faculty of Computer Engineering, Najafabad Branch, Islamic Azad University, Najafabad 66414, Iran
Teodor Bulboacă: Faculty of Mathematics and Computer Science, Babeş-Bolyai University, 400084 Cluj-Napoca, Romania

Mathematics, 2023, vol. 11, issue 9, 1-10

Abstract: The logarithmic coefficients play an important role for different estimates in the theory of univalent functions. Due to the significance of the recent studies about the logarithmic coefficients, the problem of obtaining the sharp bounds for the modulus of these coefficients has received attention. In this research, we obtain sharp bounds of the inequality involving the logarithmic coefficients for the functions of the well-known class G and investigate a majorization problem for the functions belonging to this family. To prove our main results, we use the Briot–Bouquet differential subordination obtained by J.A. Antonino and S.S. Miller and the result of T.J. Suffridge connected to the Alexander integral. Combining these results, we give sharp inequalities for two types of sums involving the modules of the logarithmical coefficients of the functions of the class G indicating also the extremal function. In addition, we prove an inequality for the modulus of the derivative of two majorized functions of the class G , followed by an application.

Keywords: univalent functions; starlike, convex and close-to-convex functions; subordination; subordination function; logarithmic coefficients (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2023
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