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Spirallike mappings and univalent subordination chains in ℂ n

Ian Graham, Hidetaka Hamada, Gabriela Kohr, Mirela Kohr (2008)

Annali della Scuola Normale Superiore di Pisa - Classe di Scienze

In this paper we consider non-normalized univalent subordination chains and the connection with the Loewner differential equation on the unit ball in ℂ n . To this end, we study the most general form of the initial value problem for the transition mapping, and prove the existence and uniqueness of solutions. Also we introduce the notion of generalized spirallikeness with respect to a measurable matrix-valued mapping, and investigate this notion from the point of view of non-normalized univalent subordination...

Starlike functions of complex order involving q-hypergeometric functions with fixed point

Kaliappan Vijaya, Gangadharan Murugusundaramoorthy, Murugesan Kasthuri (2014)

Annales Universitatis Paedagogicae Cracoviensis. Studia Mathematica

Recently Kanas and Ronning introduced the classes of starlike and convex functions, which are normalized with ƒ(ξ) = ƒ0(ξ) − 1 = 0, ξ (|ξ| = d) is a fixed point in the open disc U = {z ∈ ℂ: |z| < 1}. In this paper we define a new subclass of starlike functions of complex order based on q-hypergeometric functions and continue to obtain coefficient estimates, extreme points, inclusion properties and neighbourhood results for the function class T Sξ(α, β,γ). Further, we obtain integral means inequalities...

Starlikeness of functions satisfying a differential inequality

Rosihan M. Ali, S. Ponnusamy, Vikramaditya Singh (1995)

Annales Polonici Mathematici

In a recent paper Fournier and Ruscheweyh established a theorem related to a certain functional. We extend their result differently, and then use it to obtain a precise upper bound on α so that for f analytic in |z| < 1, f(0) = f'(0) - 1 = 0 and satisfying Re{zf''(z)} > -λ, the function f is starlike.

Starlikeness of polynomials and finite Blaschke products

Alan Gluchoff, Frederick Hartmann (2008)

Annales Polonici Mathematici

The radius of starlikeness for polynomial mappings and finite Blaschke products with zeroes distributed at equal angles around a circle centered at the origin, as well as with zeroes concentrated at a single point, are considered, and sharp bounds are obtained. Results expressing the radius of starlikeness of an arbitrary polynomial or Blaschke product in terms of the magnitudes of the zeroes are also given. These are also sharp.

Strongly gamma-starlike functions of order alpha

Mamoru Nunokawa, Janusz Sokół (2013)

Annales UMCS, Mathematica

In this work we consider the class of analytic functions G(α, γ), which is a subset of gamma-starlike functions introduced by Lewandowski, Miller and Złotkiewicz in Gamma starlike functions, Ann. Univ. Mariae Curie- Skłodowska, Sect. A 28 (1974), 53-58. We discuss the order of strongly starlikeness and the order of strongly convexity in this subclass.

Strongly starlike and spirallike functions

Adam Lecko (2005)

Annales Polonici Mathematici

The aim of this paper is to present a new method of proof of an analytic characterization of strongly starlike functions of order (α,β). The relation between strong starlikeness and spirallikeness of the same order is discussed in detail. Some well known results are reproved.

Currently displaying 101 – 120 of 178