Exploring a distinct group of analytical functions linked with Bernoulli's Lemniscate using the q-derivative

This research presents a new group of mathematical functions connected to Bernoulli's Lemniscate, using the q-derivative. Expanding on previous studies, the research concentrates on determining coefficient approximations, the Fekete-Szego functional, Zalcman inequality, Krushkal inequality, alo...

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Bibliographic Details
Published in:Heliyon 2024-07, Vol.10 (14), p.e34095, Article e34095
Main Authors: Al-Shbeil, Isra, Shaba, Timilehin Gideon, Alb Lupas, Alina, Alhefthi, Reem K.
Format: Article
Language:English
Subjects:
Bounded turning function
Fekete-Szego estimates
Hankel determinant
Krushkal inequality
q-derivative operator
Zalcman inequality
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Summary:This research presents a new group of mathematical functions connected to Bernoulli's Lemniscate, using the q-derivative. Expanding on previous studies, the research concentrates on determining coefficient approximations, the Fekete-Szego functional, Zalcman inequality, Krushkal inequality, along with the second and third Hankel determinants for this recently established collection of functions. Additionally, the study derives the Fekete-Szego inequality for the function ξf(ξ) and obtains the inverse function f−1(ξ) for this specific class. This research advances our understanding in this area and suggests for further exploration.
ISSN:2405-8440
2405-8440
DOI:10.1016/j.heliyon.2024.e34095