Abstract
The theory of q-calculus operators are applied in many areas of sciences such as complex analysis. In this paper we apply S˘al˘agean q-differential operator to harmonic functions and introduce sharp coefficient bounds, extreme points, distortion inequalities and convexity results.
Highlights
The theory of q–calculus operators are applied in many areas of sciences such as complex analysis
We state some notations regarding to q–calculus used in this article, see [1, 4] and [6]
Let Sh denote the class of functions: f =h+g which are harmonic, univalent and sense-preserving in U and normalized by f (0) = f (0) − 1 = 0, where h and g are analytic in U take the form:
Summary
We state some notations regarding to q–calculus used in this article, see [1, 4] and [6]. In this paper we apply Salagean q–differential operator to harmonic functions and introduce sharp coefficient bounds, extreme points, distortion inequalities and convexity results. Q–calculus; harmonic; univalent; Salagean operator; convex set. For f (z) = z + ∞ k=2akzk, the Salagean q–differential operator is defined by: Sq0f (z) = f (z)
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