Sharp inequalities for a class of novel convex functions associated with Gregory polynomials

This paper explores the class C G , consisting of functions g that satisfy a specific subordination relationship with Gregory coefficients in the open unit disk E . By applying certain conditions to related coefficient functionals, we establish sharp estimates for the first five coefficients of thes...

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Bibliographic Details
Published in:Journal of inequalities and applications 2024-11, Vol.2024 (1), p.140-19, Article 140
Main Authors: Srivastava, Hari. M., Cho, Nak Eun, Alderremy, A. A., Lupas, Alina Alb, Mahmoud, Emad E., Khan, Shahid
Format: Article
Language:English
Subjects:
Analysis
Analytic functions
Applications of Mathematics
Coefficient problems
Convex analysis
Convex functions
Functionals
Gregory polynomials
Investigations
Mathematics
Mathematics and Statistics
Polynomials
Subordination
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Summary:This paper explores the class C G , consisting of functions g that satisfy a specific subordination relationship with Gregory coefficients in the open unit disk E . By applying certain conditions to related coefficient functionals, we establish sharp estimates for the first five coefficients of these functions. Additionally, we derive bounds for the second and third Hankel determinants of functions in C G , providing further insight into the class’s properties. Our study also investigates the logarithmic coefficients of log ( g ( t ) t ) and the inverse coefficients of the inverse functions ( g − 1 ) within the same class.
ISSN:1029-242X
1025-5834
1029-242X
DOI:10.1186/s13660-024-03210-5