The Faber polynomial expansion method and its application to the general coefficient problem for some subclasses of bi-univalent functions associated with a certain q-integral operator

Abstract

In our present investigation, we first introduce several new subclasses of analytic and bi-univalent functions by using a certain q-integral operator in the open unit disk U = {z : z ∈ Cand |z| < 1}. By applying the Faber polynomial expansion method as well as the q-analysis, we then determine bounds for the nth coefficient in the Taylor-Maclaurin series expansion for functions in each of these newly-defined analytic and bi-univalent function classes subject to a gap series condition. We also highlight some known consequences of our main results.

Faber Polynomial Coefficient Estimates for Bi-Univalent Functions Defined by Using Differential Subordination and a Certain Fractional Derivative Operator

“…We conclude our present investigation by observing that the interested reader will find several related recent developments concerning Geometric Function Theory of Complex Analysis (see, for example, [46,[49][50][51]) to be potentially useful for motivating further researches in this subject and on other related topics. Funding: This research received no external funding.…”

Coefficient bounds for certain subclasses of bi-prestarlike functions associated with the Chebyshev polynomials

“…These polynomials have been studied in several papers from a theoretical point of view. Lately ,there has been triggering interest by introducing a new class of A and discussed coefficient problems and celebrated Fekete-Szegö problem(see [21,26,27,28]) further certain subclasses of Σ were defined by means of these polynomials(see [15,20,22,24] and discussed extensively. Here, in this article, we propose to make use of the Chebyshev polynomials, which is used by us in this paper, play a considerable act in numerical analysis.…”

Fekete-Szegö Type Problems and Their Applications for a Subclass of q-Starlike Functions with Respect to Symmetrical Points

“…Kanas and Raducanu [13] introduced the q-analogue of the Ruscheweyh operator by using the concept of convolution and studied some of its properties (see also [11,[14][15][16][17][18][19][20]). Many other q-derivative and q-integral operators can be written by using the idea of convolution (we refer, for details, to [21][22][23][24]). For a comprehensive review of the quantum (or q-)-calculus literature, we refer to a recently-published survey-cum-expository review article by Srivastava [25].…”