# On the order of starlikeness and convexity of complex harmonic functions with a two-parameter coefficient condition

Annales UMCS, Mathematica (2010)

- Volume: 64, Issue: 1, page 81-91
- ISSN: 2083-7402

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topAgnieszka Sibelska. "On the order of starlikeness and convexity of complex harmonic functions with a two-parameter coefficient condition." Annales UMCS, Mathematica 64.1 (2010): 81-91. <http://eudml.org/doc/268102>.

@article{AgnieszkaSibelska2010,

abstract = {The article of J. Clunie and T. Sheil-Small [3], published in 1984, intensified the investigations of complex functions harmonic in the unit disc Δ. In particular, many papers about some classes of complex mappings with the coefficient conditions have been published. Consideration of this type was undertaken in the period 1998-2004 by Y. Avci and E. Złotkiewicz [2], A. Ganczar [5], Z. J. Jakubowski, G. Adamczyk, A. Łazińska and A. Sibelska [1], [8], [7], H. Silverman [12] and J. M. Jahangiri [6], among others. This work continues the investigations described in [7]. Our results relate primarily to the order of starlikeness and convexity of functions of the aforementioned classes.},

author = {Agnieszka Sibelska},

journal = {Annales UMCS, Mathematica},

keywords = {Complex harmonic functions; analytic conditions; convexity of order β; starlikeness of order β; complex harmonic functions; convexity of order ; starlikeness of order },

language = {eng},

number = {1},

pages = {81-91},

title = {On the order of starlikeness and convexity of complex harmonic functions with a two-parameter coefficient condition},

url = {http://eudml.org/doc/268102},

volume = {64},

year = {2010},

}

TY - JOUR

AU - Agnieszka Sibelska

TI - On the order of starlikeness and convexity of complex harmonic functions with a two-parameter coefficient condition

JO - Annales UMCS, Mathematica

PY - 2010

VL - 64

IS - 1

SP - 81

EP - 91

AB - The article of J. Clunie and T. Sheil-Small [3], published in 1984, intensified the investigations of complex functions harmonic in the unit disc Δ. In particular, many papers about some classes of complex mappings with the coefficient conditions have been published. Consideration of this type was undertaken in the period 1998-2004 by Y. Avci and E. Złotkiewicz [2], A. Ganczar [5], Z. J. Jakubowski, G. Adamczyk, A. Łazińska and A. Sibelska [1], [8], [7], H. Silverman [12] and J. M. Jahangiri [6], among others. This work continues the investigations described in [7]. Our results relate primarily to the order of starlikeness and convexity of functions of the aforementioned classes.

LA - eng

KW - Complex harmonic functions; analytic conditions; convexity of order β; starlikeness of order β; complex harmonic functions; convexity of order ; starlikeness of order

UR - http://eudml.org/doc/268102

ER -

## References

top- Adamczyk, G., Łazińska, A., On some generalization of coefficient conditions for complex harmonic mappings, Demonstratio Math. 38 (2) (2004), 317-326. Zbl1071.30004
- Avci, Y., Złotkiewicz E., On harmonic univalent mappings, Ann. Univ. Mariae Curie-Skłodowska Sec. A. 44 (1) (1990), 1-7.
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- Jakubowski, J. Z., Łazińska, A. and Sibelska, A., On some properties of complex harmonic mappings with a two-parameter coefficient condition, Math. Balkanica, New Ser. 18 (2004), 313-319. Zbl1094.30018
- Łazińska, A., On complex mappings in the unit disc with some coefficient conditions, Folia Sci. Univ. Techn. Resoviensis 199 (26) (2002), 107-116. Zbl1196.30011
- Mocanu, S. S., Miller, P. T., Differential Subordinations: Theory and Applications, Marcel Dekker, New York and Basel, 2000. Zbl0954.34003
- Pinchuk, B., Starlike and convex functions of order α, Duke Math. J. 35 (4) (1968), 721-734. Zbl0167.36101
- Robertson, M., On the theory of univalent functions, Ann. of Math. 37 (1936), 374-408. Zbl62.0373.05
- Silverman, H., Harmonic univalent functions with negative coefficients, J. Math. Anal. Appl. 220 (1998), 283-289. Zbl0908.30013

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