On a subclass of bi-univalent functions associated with the q-derivative operator

Abstract

In this paper, we consider a new subclass of analytic and bi-univalent functions associated with q-Ruscheweyh differential operator in the open unit disk U. For functions belonging to the class Σ q (λ, φ), we obtain estimates on the first two Taylor-Maclaurin coefficients. Further, we derive another subclass of analytic and bi-univalent functions as a special consequences of the results.

Maclaurin Coefficient Estimates of Bi-Univalent Functions Connected with the q-Derivative

“…These classes will be introduced by using the subordination and the results are obtained by employing the techniques used earlier by Srivastava et al [10]. This last work represents one of the most important study of the bi-univalent functions, and inspired many investigations in this area including the present paper, while many other recent papers deal with problems initiated in this work, like [13][14][15][16], and many others. The novelty of our paper consists of the fact that the operator used by defining the new subclass of Σ is a very general operator that generalizes many earlier defined operators, it does not overlap with those studied in the above mentioned papers (that Φ (0) > 0 and Φ(U) is symmetric with respect to the real axis), while for the function Φ from Definition 1 we did not assume any restrictions like in many other papers, excepting the fact that Φ(0) = 1 is necessary for the subordinations (13) and (14).…”

Faber polynomial coefficient estimates of bi-close-to-convex functions connected with the Borel distribution of the Mittag-Leffler type

“…[21] such as, for example, [25,26,27,28,29] (see also [30,31,32,33] and the references to other related developments which are cited in each of these publications). Motivated by the earlier work of Sakar and Güney [34], we define the following subclass of bi-close-to-convex functions M α,β ,λ Σ (γ, ϑ ) related with the Mittag-Leffler type Borel distribution.…”

Faber Polynomial Coefficient Estimates of Bi-Close-to-Convex Functions Associated with Generalized Hypergeometric Functions

“…The widely cited paper by Srivastava et al [3] not only represents one of the most important studies of bi-univalent functions, but it also resuscitated the study of bi-univalent functions in recent years. Many subsequent papers investigated the problems concerned with bi-univalent functions, such as [9][10][11][12].…”