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

In this article we introduce three new subclasses of the class bi-univalent functions Σ, namely HGΣ, GMΣ(μ) and GΣ(λ), by using subordinations with whose coefficients are Gregory numbers. First, evidence that these classes not empty, i.e., they contain other besides identity one. For in each function classes, investigate estimates a2 a3 Taylor–Maclaurin Fekete–Szegő functional problems. The main results followed some particular cases, novelty characterizations proofs may lead to further studies such types similarly defined analytic functions.