On classes of meromorphic or complex harmonic functions with a pole at the infinity

• Autorzy: Jakubowski Z. , Sibelska A.
• Języki publikacji: EN

Abstrakty

EN

In this article we investigate some classes of meromorphic or complex harmonie functions with a pole, which are generated either by analytic conditions or by "coefficient inequalities". There are given theorems, which combine the geometrical properties of functions of the introduced classes. Some results broaden knowledge about the classes of functions, which were investigated in [15]. The main inspiration for the reaserch were the papers [4] and [11]. The part of results were presented in the XII-th International Mathematically-Informatical Conference in Chełm (2nd-5th July, 2006) [12].

Słowa kluczowe

EN

meromorphic functions; starlike functions; convex functions

PL

funkcje harmoniczne; funkcje gwiaździste; funkcje wypukłe

• Wydawca: De Gruyter
• Czasopismo: Demonstratio Mathematica
• Rocznik: 2009
• Tom: Vol. 42, nr 3
• Strony: 479--489
• Opis fizyczny: Bibliogr. 15 poz.

Twórcy

autor

Jakubowski Z.

autor

Sibelska A.

• Department of Nonlinear Analysis Faculty of Mathematics and Computer Science University of Łódź ul. S. Banacha 22 90-238 Łódź, Poland,

Bibliografia

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• [3] J. Becker, Über holömorphe fortsetzung schlichter Funktionen, Ann. Acad. Sci. Fenn. 538 (1973), 2-11.
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• [5] P. Duren, Univalent Functions, Springer-Verlag, New York-Berlin-Heidelberg-Tokyo (1983).
• [6] R. M. Goel, A class of close-to-convex functions, Czechoslovak Math. J. 18 (93) (1968), 104-116.
• [7] J. S. Hadamard, Théorème sur les séries entières, Acta Math. 22 (1898), 55-65.
• [8] J. M. Jahangiri, H. Silverman, Meromorphic univalent harmonic functions with negative coefficients, Bull. Korean. Math. Soc. 36 (4) (1999), 763-770.
• [9] Z. J. Jakubowski, On some applications of the Clunie method, Ann. Polon. Math. 26 (1972), 211-217.
• [10] Z. J. Jakubowski, On the coefficients of Caratheodory functions, Bull. Polish Acad. Sci. Math. 19, 9 (1971), 805-809.
• [11] Z. J. Jakubowski, A. Łazińska, On some harmonic functions related to holomorfic functions with a positive real part, Tr. Petrozavodsk. Gos. Univ., Ser. Mat. 13 (2004), 61-70.
• [12] Z. J. Jakubowski, A. Sibelska, On classes of holomorphic and complex harmonic functions with a pole at the infinity generate by some analytic conditions (in Polish), Conference papers of the XII Environmental Mathematically-Informatical Conference, Chełm, (2006), 20-21.
• [13] T. H. Mac Gregor, The radius of convexity for starlike functions of order 1/2, Proc. Amer. Math. Soc. 14 (1963), 71-76.
• [14] T. H. Mac Gregor, The radius of univalence of certain analytic functions, Proc. Amer. Math. Soc. 14 (1963), 514-520, 521-524.
• [15] A. Sibelska, On some coefficient conditions for complex harmonic functions with a pole at the infinity, Demonstratio Math. 39 (2006), 335-346.