Initial Coefficient Bounds for Bi-Univalent Functions Related to Gregory Coefficients

Gangadharan Murugusundaramoorthy, Kaliappan Vijaya and Teodor Bulboacă ()
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Gangadharan Murugusundaramoorthy: Department of Mathematics, Vellore Institute of Technology (VIT), Vellore 632014, TN, India
Kaliappan Vijaya: Department of Mathematics, Vellore Institute of Technology (VIT), Vellore 632014, TN, India
Teodor Bulboacă: Faculty of Mathematics and Computer Science, Babeş-Bolyai University, 400084 Cluj-Napoca, Romania

Mathematics, 2023, vol. 11, issue 13, 1-16

Abstract: In this article we introduce three new subclasses of the class of bi-univalent functions Σ , namely HG Σ , GM Σ ( μ ) and G Σ ( λ ) , by using the subordinations with the functions whose coefficients are Gregory numbers. First, we evidence that these classes are not empty, i.e., they contain other functions besides the identity one. For functions in each of these three bi-univalent function classes, we investigate the estimates a 2 and a 3 of the Taylor–Maclaurin coefficients and Fekete–Szegő functional problems. The main results are followed by some particular cases, and the novelty of the characterizations and the proofs may lead to further studies of such types of similarly defined subclasses of analytic bi-univalent functions.

Keywords: univalent functions; bi-univalent functions; starlike and convex functions of some order; subordination; Fekete–Szeg? problem (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2023
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