Fekete-Szego problem for certain analytic functions defined by q−derivative operator with respect to symmetric and conjugate points

Abstract

Recently, the q−derivative operator has been used to investigate several subclasses of analytic functions in different ways with different perspectives by many researchers and their interesting results are too voluminous to discuss. For example, the extension of the theory of univalent functions can be used to describe the theory of q−calculus, q−calculus operator are also used to construct several subclasses of analytic functions and so on. In this work, we considered the Fekete-Szego problem for certain analytic functions defined by q−derivative operator with respect to symmetric and conjugate points. The early few coefficient bounds were obtained to derive our results.

The Subclasses of Analytic Functions of Complex Order with Application of q-Derivative Operators

“…Further, if q → 1 − , the class S * q (𝛾) and C q (𝛾) reduces to the starlike functions of order 𝛾, S * (𝛾), and convex functions of order 𝛾, C (𝛾), respectively. Furthermore, there are several new subclasses of A involving q-derivative that have been introduced by other mathematicians (see Aldweby and Darus, 2017;Alsoboh and Darus, 2019;Altinkaya and Yalçin, 2017;Bulut, 2017;Janteng and Halim, 2009b;Karahuseyin, 2017;Lashin et al, 2021;Hern et al, 2022;Hern et al, 2020;Olatunji and Dutta, 2018;Piejko and Sokół, 2020;Ramachandran et al, 2017;Shamsan et al, 2021;Shilpa, 2022). In fact Seoudy and Aouf (2016) have introduced how classes of q-convex and q-starlike of complex order can be obtained using the principle of subordination and q-derivative.…”

Coefficient problems for classes Hq (φ) and Lq (φ)

“…An earlier time, certain researchers discussed about the coefficient estimate which is F-S functional for various type of subclasses of M . After that, some of them started to study the subclasses associated the q -derivative operator (see [3][4][5][6][7]). For example, in [3], they discussed about the bounds of F-S functional of starlike and convex functions regarding the q-derivative.…”

“…For example, in [3], they discussed about the bounds of F-S functional of starlike and convex functions regarding the q-derivative. While in [4], the authors found the F-S functional for the function belongs to the class of symmetric and conjugate points. Paper [5] shows the results from some others interesting subclasses, while the authors in [6] discussed q-starlike and q-convex functions of complex order.…”