A Class of Rational Mappings in Several Complex Variables

Abstract

Abstract. In this paper, we will give coefficient conditions for mappings of the form /(z) = z/(l+Er=i ) to be starlike or convex on the Euclidean unit ball B in C™. Our results give concrete examples of strongly starlike mappings of order a, starlike mappings of order a and convex mappings on B.

Starlike and convex rational mappings on infinite dimensional domains

“…Indeed, given a holomorphic function g(ζ) = 1 + ∞ k=1 a k ζ k , Reade-Silverman-Todorov [14], Obradović [10], Obradović-Ponnusamy-Singh-Vasundhra [11] and Ponnusamy-Vasundhra [13] have obtained conditions on the coefficients a k for ζ/g(ζ) to be starlike of order α (0 ≤ α ≤ 1) or convex of order β (0 ≤ β < 1). These results have been extended to the Euclidean unit ball in C n by Hamada-Kohr [7]. In this paper, we consider rational mappings of the form z/g(z) defined on infinite dimensional domains, where g(z) is given by an infinite series 1 + ∞ k=1 a k ζ k .…”