In this paper, we introduce and investigate a novel class of analytic and univalent functions with negative Taylor-Maclaurin coefficients in the open unit disk. For this function class, we obtain characterization and distortion theorems as well as the radii of close-to-convexity, starlikeness and convexity by using techniques involving operators of fractional calculus.

No abstract

In this paper, we introduce and investigate a newly-constructed class of univalent functions in the open disk. For this function class, we obtain upper bounds for the second Hankel determinant [Formula: see text].

Making use of the λ-pseudoq-differential operator, we aim to investigate a new, interesting class of bi-starlike functions in the conic domain. Furthermore, we obtain certain sharp bounds of the Fekete-Szegö functional for functions belonging to this class.

In the present work, we propose to introduce and investigate a new class SLΣq,μ (γ, λ, n, pκ) of the function class Σ of bi-univalent functions related to κ-Fibonacci numbers defined in the open unit disk, which is associated with the Salagean type q-difference operator and satisfy some subordination conditions. We obtain coefficient bounds for the Taylor–Maclaurin coefficients |a2| and |a3| of the functions in the new class. Furthermore, we solve the Fekete–Szegö functional for functions in the class SLΣq,μ (γ, λ, n, pκ).