Faber Polynomial Coefficient Estimates for Bi-Close-to-Convex Functions Defined by the q-Fractional Derivative

Abstract

By utilizing the concept of the q-fractional derivative operator and bi-close-to-convex functions, we define a new subclass of A, where the class A contains normalized analytic functions in the open unit disk E and is invariant or symmetric under rotation. First, using the Faber polynomial expansion (FPE) technique, we determine the lth coefficient bound for the functions contained within this class. We provide a further explanation for the first few coefficients of bi-close-to-convex functions defined by the q-fractional derivative. We also emphasize upon a few well-known outcomes of the major findings in this article.

Estimating the Second Order Hankel Determinant for the Subclass of Bi-Close-to-Convex Function of Complex Order

“…We now investigate the maximization of the function F (α, γ) over the closed square region of the Analytically by looking at the expressions in (36), we see that Q 3 < 0 and Q 3 + 2Q 4 > 0 for b ∈ (0, 2), consequently we get…”

“…Srivastava et al [34] applied the Faber polynomial expansion method to estimate the coefficient of general Taylor-Maclaurin series and the Fekete-Szegö type inequalities for the class of bi-close-to-convex function. A new subclass of bi-close-to-convex functions associated with the generalized hypergeometric functions, q-fractional derivative operator and with bounded boundary rotation is recently studied by [6,36] and coefficient estimates of bi-close-to-convex functions associated with generalized hypergeometric functions for Faber polynomial were studied by Jie et al [41].…”

Subclasses of Noshiro-Type Starlike Harmonic Functions Involving q-Srivastava–Attiya Operator

“…Or the Srivastava-Attiya operator can be extended to the domain of control system analysis where the field of vector space is complex in C 2 (U) in some cases for future works, such as in [48]. The operator introduced in this article can also be applied to extend the study on various subclasses of bi-univalent functions, meromorphic functions and symmetric functions [49][50][51][52]. By using the Miller-Ross-type Poisson distribution series (see [53] and references cited therein), one can also study certain inclusion results for HS κ,℘ q ( , ℵ).…”

Bi-Concave Functions Connected with the Combination of the Binomial Series and the Confluent Hypergeometric Function

“…In this article, we have considered the coefficient estimate problems for the initial Taylor-Maclaurin coefficients for functions in some specified subclasses of the class of analytic and bi-concave functions in Λ. It would be of interest to investigate the applications of the Faber polynomial expansion method (see [25,26]) in order to tackle the coefficient estimate problems for the general Taylor-Maclaurin coefficients for these and other subclasses of the class of analytic and bi-concave functions (see, for details, [27][28][29]; see also [30] and the references to the earlier literature on the subject, which are cited in each of these works).…”