Abstract
In this paper, we introduce new subclasses of the function classΣof bi-univalent functions connected with aq-analogue of Bessel function and defined in the open unit disc. Furthermore, we find estimates on the first two Taylor-Maclaurin coefficientsa2anda3for functions in these new subclasses.
Highlights
We introduce new subclasses of the function class Σ of bi-univalent functions connected with a q-analogue of Bessel function and defined in the open unit disc
We find estimates on the first two Taylor-Maclaurin coefficients ja2j and ja3j for functions in these new subclasses
Jackson was the first to have some applications of the q-calculus and introduced the q-analogue of the classical derivative and integral operators
Summary
Received 10 January 2020; Revised 20 February 2020; Accepted 28 April 2020; Published 22 May 2020. We introduce new subclasses of the function class Σ of bi-univalent functions connected with a q-analogue of Bessel function and defined in the open unit disc. We find estimates on the first two Taylor-Maclaurin coefficients ja2j and ja3j for functions in these new subclasses. F ðzÞ = z + 〠 akzk, z ∈ Δ ≔ fz ∈ C : jzj < 1g, ð1Þ k=2 and S be the subclass of A which are univalent functions in Δ. The Bessel function of the first kind of orderν is defined by the infinite series (see [6]). Szász and Kupán [7] investigated the univalence of the normalized Bessel function of the first kind kν : Δ ⟶ C defined by (see [8,9,10])
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Free) 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a call
