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Abstrakty
In the paper there are determined, for some classes defined by coefficient or analytic conditions, the sets of complex parameter γ, for which all the functions of the appropriate family have some geometrical properties. There are also provided the examples of the mappings showing that some inclusions between classes are impossible or confirming that sets of the parameter γ cannot be extended in some cases without loss of these geometric properties.
Wydawca
Czasopismo
Rocznik
Tom
Strony
77--85
Opis fizyczny
Bibliogr. 11 poz.
Twórcy
autor
- Faculty of Mathematics and Computer Science, University of Łódź, ul. S. Banacha 22, 90-238 Łódź, Poland
Bibliografia
- [1] G. Adamczyk and A. Łazińska, On some generalization of coefficient conditions for complex harmonic mappings, Demonstratio Math. 38 (2004), no. 2, 317-326.
- [2] Y. Avci and E. Złotkiewicz, On harmonic univalent mappings, Ann. Univ. Mariae Curie-Sklodowska Sect. A 44 (1990), no. 1, 1-7.
- [3] J. Clunie and T. Sheil-Small, Harmonic univalent mappings, Ann. Acad. Sci. Fenn. Ser. A I Math. 9 (1984), 3-25.
- [4] J.M. Jahangiri, Harmonic functions starlike in the unit disk, J. Math. Anal. Appl. 235 (1999), 470-477.
- [5] Z. J. Jakubowski, A. Łazińska and A. Sibelska, On some properties of complex harmonic mappings with a two-parameter coefficient condition, Math. Balkanica (N.S.) 18 (2004), 313-319.
- [6] A. Łazińska, On complex mappings in the unit disc with some coefficient conditions, Folia Sci. Univ. Techn. Resoviensis 199 (2002), 107-116.
- [7] A. Sibelska, On the order of starlikeness and convexity of complex harmonic functions with a two-parameter coefficient condition, Ann. Univ. Mariae Curie-Sklodowska Sect. A 54 (2010), no. 1, 81-91.
- [8] H. Silverman, Harmonic univalent functions with negative coefficients, J. Math. Anal. Appl. 220 (1998), 283-289.
- [9] H. Silverman and E. Silvia, Subclasses of harmonic univalent functions, New Zealand J. Math. 28 (1999), 275-284.
- [10] J. Stankiewicz and J. Waniurski, Some classes of functions subordinate to linear transformation and their applications, Ann. Univ. Mariae Curie-Sklodowska Sect. A 28 (1974), no. 9, 85-94.
- [11] S. Yalçin and M. Öztürk, Harmonic functions starlike of the complex order, Math. Vesn. 58 (2006), 7-11.
Typ dokumentu
Bibliografia
Identyfikator YADDA
bwmeta1.element.baztech-c137b49b-96b4-4a20-bf47-cd76f41ca91b