A NOVEL CLASS OF MULTIVALENTLY ANALYTIC FUNCTIONS WITH NEGATIVE COEFFICIENTS AND ITS APPLICATIONS

Year 2002, Volume: 4 Issue: 2, 83 - 92, 01.12.2002

Faruk Çetin

Abstract

A novel class Tλ(p, n,α ) of multivalently analytic functions wiht negative coeffiicients, and some interesting properties belonging to the this class is obtained.

Keywords

Analytic , multivalent , close-to-convex , starlike , and convex functions , coefficienta bounds , growth and distortion theorems , and fractional calculu

NEGATİF KATSAYILI ÇOK DEĞERELİ ANALİTİK FONKSİYONLARIN YENİ BİR SINIFI VE UYGULAMALARI

Abstract

A novel class T( p,n,a) αλ,,npT of multivalently analytic functions wiht negative coeffiicients, and some interesting properties belonging to the this class is obtained.

Keywords

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References

• P. L. Duren, Univalent Functions, Grunlehren der mathematischen wissenschaften, Bd.
• , Springer-Verlag, New York, Berlin, Heiderberg, and Tokyo, 1983.
• A. W. Goodman, Univalent Functions, Vols. I and II, Polygonal Publishing Conpany Washington, New Jersey, 1983.
• H. M. Srivastava and S. Owa (Editors), Current topics in analitic function theory, Word Scientific Publishing Company, Singapure, New Jersey, London, and Hong Kong, 1992.
• O. Altıntaş, H. Irmak and H. M. Srivastava, Fractional calculus and certain starlike functions with negative coefficients, Comput Math. Appl. 30 (2) (1995), 9-15.
• M. -P. Chen, H. Irmak and H. M. Srivastava, Some multivalently functions with negative coefficients defined by using a differantial operator, Pan Amer. Math. J. 6 (2) (1996), 55-64.
• M. -P. Chen, H. Irmak and H. M. Srivastava, Some families of multivalently analytic functions with negative coefficients, J. Math. Anal. Appl. 214 (2) (1997), 674-690.
• H. Irmak, Certain subclasses of p-valently starlike functions with negative coefficient,
• Bull. Calcutta Math. Soc. 87 (1995), 589-598.
• H. Irmak, S. H. Lee, and N. E. Cho, Some multivalently analytic functions with negative coefficients and their subclasses defined by using a differantial operators, Kyungpook Maht. J. 37 (1) (1997), 43-51.
• M. K. Aouf and H. M. Srivastava, A certain fractional derivative operator and it's application to the new class of anallytic and multivalent with negative coefficient. I and II, J. Math. Anal. Appl. 171 (1992), ibid (1995),673-688.
• S. Owa, On the distortion theorems. I, Kyungpook Maht. J., 18 (1978), 53-59. [11] S. Owa and H. M. Srivastava, Univalent and starlike generalized hypergeometric
• function, Canad. J. Math., 39 (1987), 1057-1077.