Sharp Coefficient Estimates for Analytic Functions Associated with Lemniscate of Bernoulli

Rubab Nawaz (), Rabia Fayyaz, Daniel Breaz and Luminiţa-Ioana Cotîrlă
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Rubab Nawaz: Department of Mathematics, COMSATS University Islamabad, Islamabad 44000, Pakistan
Rabia Fayyaz: Department of Mathematics, COMSATS University Islamabad, Islamabad 44000, Pakistan
Daniel Breaz: Department of Mathematics, “1 Decembrie 1918” University of Alba Iulia, 510009 Alba Iulia, Romania
Luminiţa-Ioana Cotîrlă: Department of Mathematics, Technical University of Cluj-Napoca, 400114 Cluj-Napoca, Romania

Mathematics, 2024, vol. 12, issue 15, 1-24

Abstract: The main purpose of this work is to study the third Hankel determinant for classes of Bernoulli lemniscate-related functions by introducing new subclasses of star-like functions represented by S L λ * and R L λ . In many geometric and physical applications of complex analysis, estimating sharp bounds for problems involving the coefficients of univalent functions is very important because these coefficients describe the fundamental properties of conformal maps. In the present study, we defined sharp bounds for function-coefficient problems belonging to the family of S L λ * and R L λ . Most of the computed bounds are sharp. This study will encourage further research on the sharp bounds of analytical functions related to new image domains.

Keywords: analytic function; univalent function; star-like functions; Schwarz function; Bernoulli’s lemniscate (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2024
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