A class of rational mappings in several complex variables

• Autorzy: Hamada H. , Kohr G.
• Języki publikacji: EN

Abstrakty

EN

In this paper, we will give coefficient conditions for mappings of the form f(z) = z/(1+sum for k=1 bkzk1 to infinity) to be starlike or convex on the Euclidean unit ball B in Cn. Our results give concrete examples of strongly starlike mappings of order a, starlike mappings of order a and convex mappings on B.

Słowa kluczowe

EN

convex mappings; rational mappings; starlike mappings

PL

odwzorowanie gwiaździste; odwzorowanie wymierne; odwzorowanie wypukłe

• Wydawca: De Gruyter
• Czasopismo: Demonstratio Mathematica
• Rocznik: 2005
• Tom: Vol. 38, nr 2
• Strony: 323--330
• Opis fizyczny: Bibliogr. 9 poz.

Twórcy

autor

Hamada H.

• Faculty of Engineering, Kyushu Sangyo University, 3-1 Matsukadai 2-Chome, Higashi-ku, Fukuoka 813-8503, Japan

autor

Kohr G.

• Faculty of Mathematics and Computer Science, Babeș-Bolyai University, 1 M. Kogălniceanu Str., 3400 Cluj-Napoca, Romania

Bibliografia

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• [3] H. Hamada, G. Kohr, Φ-like and convex mappings in infinite dimensional spaces, Rev. Roumaine Math. Pures Appl. 47 (2002), 315-328.
• [4] K. Kikuchi, Starlike and convex mappings in several complex variables, Pacific J. Math. 44 (1973), 569-580.
• [5] M. Obradović, Starlikeness and certain class of rational functions, Math. Nachr. 175 (1995), 263-268.
• [6] M. Obradović, S. Ponnusamy, New criteria and distortion theorems for univalent functions, Complex Variables 44 (2001), 173-191.
• [7] M. Obradović, S. Ponnusamy, V. Singh, P. Vasundhra, Univalency, starlikeness and convexity applied to certain classes of rational functions, Analysis 22 (2002), 225-242.
• [8] M. O. Reade, H. Silverman, P. G. Todorov, Classes of rational functions, Contemporary Math. 38 (1985), 99-103.
• [9] T. J. Suffridge, The principle of subordination applied to functions of several variables, Pacific J. Math. 33 (1970), 241-248.