Abstract
In this article, by using the concept of the quantum (or q-) calculus and a general conic domain Ω k , q , we study a new subclass of normalized analytic functions with respect to symmetrical points in an open unit disk. We solve the Fekete-Szegö type problems for this newly-defined subclass of analytic functions. We also discuss some applications of the main results by using a q-Bernardi integral operator.
Highlights
Introduction and DefinitionsLet A denote the class of all functions f which are analytic in the open unit diskE = {z : z ∈ C and | z | < 1}and has the normalized Taylor-Maclaurin series expansion of the following form: ∞ f (z) = z + ∑ an zn . (1) n =2Mathematics 2020, 8, 842; doi:10.3390/math8050842 www.mdpi.com/journal/mathematicsLet S be the subclass of all functions in A that are univalent in E: If f and g ∈ A, the function f is said to be subordinate to the function g, written as f ≺ g, if there exists an analytic function w in E, with w (0) = 0 and
Let P denote the well-known Carathéodory class of functions p, which are analytic in the open unit disk E with
Ωk,q, we focus on the Hankel determinant, the Toeplitz matrices and the Fekete-Szegö problems for the function class Ss∗ (q)
Summary
Let A denote the class of all functions f which are analytic in the open unit disk. and has the normalized Taylor-Maclaurin series expansion of the following form:. Kanas et al (see [4,5]; see [6]) defined and studied classes of k-starlike functions and k-uniformly convex functions subject to the conic domain Ωk (k = 0), where n o. The upper bound of the third Hankel determinant for a class of q-starlike functions was investigated in [12] (see [9]). Ωk,q and the quantum (or q-) calculus to define and investigate new subclasses of starlike functions with respect to symmetrical points in the open unit disk E. Making use of the quantum (or q-) calculus and the principle of subordination, we define q-starlike and q-convex functions with respect to symmetrical points as follows.
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