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 mai...

By using q-convolution, we determine the coefficient bounds for certain symmetric subclasses of analytic functions complex order, which are introduced here by means a non-homogeneous Cauchy–Euler-type differential equation order m.

In the present work, the author determines some coefficient bounds for functions in a new class of analytic and bi-univalent functions, which are introduced by using of polylogarithmic functions. The presented results in this paper one the generalization of the recent works of Srivastava et al. [26], Frasin and Aouf [13] and Siregar and Darus [25].

Bounds of association coefficients for binary variables are derived using the arithmetic-geometric-harmonic mean inequality. More precisely, it is shown which presence/absence coefficients are bounds with respect to each other. Using the new bounds it is investigated whether a coefficient is in general closer to either its upper or its lower bound.