Class of Analytic Functions Defined by q-Integral Operator in a Symmetric Region

Abstract

The aim of the present paper is to introduce a new class of analytic functions by using a q-integral operator in the conic region. It is worth mentioning that these regions are symmetric along the real axis. We find the coefficient estimates, the Fekete-Szegö inequality, the sufficiency criteria, the distortion result, and the Hankel determinant problem for functions in this class. Furthermore, we study the inverse coefficient estimates for functions in this class.Let f and g be analytic functions in D. Then, f is said to be subordinate to g, written as f (z) ≺ g(z), if there exists a function w analytic in D with w(0) = 0 and |w (z) | < 1 such that f (z) = g(w(z)). Moreover, if g is univalent in D, then the following equivalent relation holds:The classes of k-uniformly starlike and k-uniformly convex functions were introduced by Kanas and Wiśniowska [1,2]. A function f ∈ S is in k − ST , if and only if:

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