Sibel YALÇIN, Waggas Galib ATSHAN, Enaam Hadi ABD

Hipergeometrik Fonksiyonu İçeren Harmonik Tek Değerlikli Fonksiyonların Altsınıflarının Bir Uygulaması

Bu makalenin amacı, hipergeometrik fonksiyonları içeren belirli konvolusyon operatörünü uygulayarak harmonik univalent fonksiyonların çeşitli altsınıfları arasında bağlantılar kurmaktır. Bu tür bağlantılar açık birim disk U da Goodman-Salagean tipli harmonik univalent fonksiyonları ile araştırılmıştır.

An Application of Subclasses of Harmonic Univalent Functions Involving Hypergeometric Function

The main purpose of this paper is to establish connections between various subclasses of harmonic univalent functions by applying certain convolution operator involving hypergeometric functions. We investigate such connections with Goodman- Salagean-Type harmonic univalent functions in the open unit disc U.

PDF

___

[1] Hohlov, Y.E., Convolution operators preserving univalent functions, Ukrainian Mathematical Journal, 37, 220-226, 1985.
[2] de Branges, L., A proof of the Bieberbach conjecture, Acta Mathematica, 154, 137- 152, 1985.
[3] Ahuja, O.P., Connections between various subclasses of planar harmonic mappings Involving hypergeometric functions , Applied Mathematics and Computation, 198 (1), 305-316, 2008.
[4] Carleson, B.C., Shaffer, D.B., Starlike and prestarlike hypergeometric functions, SIAM Journal on Mathematical Analysis, 15, 737-745, 1984.
[5] Owa, S., Srivastava, H.M., Univalent and starlike generalized hypergeometric functions, Canadian Journal of Mathematics, 39, 1057-1077, 1987.
[6] Miller, S., Mocanu, P.T., Univalence of Gaussian and confluent hypergeometric Functions, Proceedings of American Mathematical Society, 110(2), 333-342, 1990.
[7] Ruscheweyh, S., Singh, V., On the order of starlikeness of hypergeometric functions, Journal of Mathematical Analysis and Applications, 113, 1-11, 1986.
[8] Srivastava, H.M., Manocha, H.L., A Treatise on Generating Functions, Ellis Horwood Limited and John Wiley & Sons, New York, Chichester, Toronto, 1984.
[9] Swaminathan, A., Certain Sufficiency conditions on Gaussian hypergeometric functions, Journal of Inequalities in Pure and Applied Mathematics, 5(4), Article 83, 1-10, 2004.
[10] Ahuja, O.P., Planar harmonic convolution operators generated by hypergeometric functions, Integral Transforms and Special Functions, 18 (3), 165-177, 2007.
[11] Clunie, J., Sheil-Small, T., Harmonic univalent functions, Annales Academie Scientiarum Fennice, Series A. I. Mathematica 9, 3-25, 1984.
[12] Ahuja, O.P., Planar harmonic univalent and related mappings, Journal of Inequalities in Pure and Applied Mathematics, 6(4) Art. 122, 1-18, 2005.
[13] Duren, P., Harmonic Mappings in the plane, Cambridge Tracts in Mathematics, Vol. 156, Cambridge University Press, Cambridge, 2004, ISBN 0-521064121-7.
[14] Ahuja, O.P., Jahangiri J.M., Noshiro-type harmonic univalent functions, Scientiae Mathematicae Japonicae, 6(2), 253-259, 2002.
[15] Aghalary, R., Goodman-Salagean-Type Harmonic Univalent Functions with Varying Arguments, International Journal of Mathematical Analysis, Vol. 1, no. 22, 1051-1057, 2007.
[16] Wang, X.T., Liang, X.Q., Zhang, Y.L., Precise coefficient estimates for close-to- convex harmonic univalent mappings, Journal of Mathematical Analysis and Applications, 263(2), 501-509, 2001.