A. L. PATHAK, R. AGARWAL, S.B. JOSHI, Preeti DWIVEDI

Subclass of harmonic univalent functions associated with the derivative operator

In the present paper, we introduce a new subclass of harmonic func- tions in the unit disc U by using the derivative operator. Also, we obtain coefficient conditions, convolution conditions, convex combina- tions, extreme points and some other properties.

PDF

___

[1] Ahuja, O. P. Planar harmonic univalent and related mappings, J. Inequal. Pure Appl. Math. 6(4), Art. 122, 1-18, 2005.
[2] Al-Shaqsi, K. and Darus, M. On harmonic functions defined by derivative operator, Journal of Inequalities and Applications, Art. ID 263413, 1-10, 2008.
[3] Al-Shaqsi, K. and Darus, M. An operator defined by convolution involving the polyloga-rithms functions, Journal of Math, and Stat. 4(1), 46-50, 2008.
[4] Clunie, J. and Sheil-Small, T. Harmonic univalent functions, Ann. Acad. Sci. Fen. Series AI Math. 9 (3), 3-25, 1984.
[5] Duren, P. Harmonic Mappings in the Plane (Cambridge Univ. Press, Cambridge, UK, 2004).
[6] Jahangiri, J. M. Harmonic functions starlike in the unit disc, J. Math. Anal. Appl. 235, 470-477, 1999.
[7] Jahangiri, J. M., Murugusundaramoorthy, G. and Vijaya, K. Salagean-type harmonic univalent functions, Southwest J. Pure Appl. Math. 2, 77-82, 2002.
[8] Murugusundaramoorthy, G. and Vijaya, K. On certain classes of harmonic univalent functions involving Ruscheweyh derivatives, Bull. Cal. Math. Soc. 96(2), 99-108, 2004.
[9] Ponnusamy, S. and Rasila, A. Planar harmonic mappings, RMS Mathematics Newsletter 17(2) (2007), 40-57, 2007.
[10] Rosy, T., Stephen, B. A., Subramanian, K. G. and Jahangiri, J.M. Goodman-Ronning-type harmonic univalent functions, Kyungpook Math. J. 41 (1), 45-54, 2001.
[11] Ruscheweyh, S. Neighborhoods of univalent functions, Proc. Amer. Math. Soc. 81, 521-528, 1981.
[12] Ruscheweyh, S. Convolutions in Geometric Function Theory (Les Presses de I Üniversite de Montreal, 1982).
[13] Sheil-Small, T. Constants for planar harmonic mappings, J. London Math. Soc. 2(42), 237-248, 1990.
[14] Silverman, H. Harmonic univalent functions with negative coefficients, J. Math. Anal. Appl. 220, 283-289, 1998.
[15] Silverman, H. and Silvia, E. M. Subclasses of harmonic univalent functions, New Zealand J. Math. 28, 275-284, 1999.
[16] Srivastava, H. M. and Owa, S. Current Topics in Analytic Function Theory (World Scientific Publishing Company, Singapore, 1992).