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SUBCLASSES OF k-UNIFORMLY CONVEX AND k-STARLIKE FUNCTIONS DEFINED BY SĂLĂGEAN OPERATOR

  • Seker, Bilal (DEPARTMENT OF MATHEMATICS FACULTY OF SCIENCE AND LETTERS BATMAN UNIVERSITY) ;
  • Acu, Mugur (DEPARTMENT OF MATHEMATICS LUCIAN BLAGA UNIVERSITY) ;
  • Eker, Sevtap Sumer (DEPARTMENT OF MATHEMATICS FACULTY OF SCIENCE DICLE UNIVERSITY)
  • Received : 2009.06.16
  • Published : 2011.01.31

Abstract

The main object of this paper is to introduce and investigate new subclasses of normalized analytic functions in the open unit disc $\mathbb{U}$, which generalize the familiar class of k-starlike functions. The various properties and characteristics for functions belonging to these classes derived here include (for example) coefficient inequalities, distortion theorems involving fractional calculus, extreme points, integral operators and integral means inequalities.

Keywords

References

  1. P. L. Duren, Univalent Functions, Springer-Verlag, New York, 1983.
  2. A. W. Goodman, On uniformly convex functions, Ann. Polon. Math. 56 (1991), no. 1, 87-92.
  3. A. W. Goodman, On uniformly starlike functions, J. Math. Anal. Appl. 155 (1991), no. 2, 364-370. https://doi.org/10.1016/0022-247X(91)90006-L
  4. S. Kanas and A. Wisniowska, Conic regions and k-uniform convexity, J. Comput. Appl. Math. 105 (1999), no. 1-2, 327-336. https://doi.org/10.1016/S0377-0427(99)00018-7
  5. S. Kanas and A. Wisniowska, Conic domains and starlike functions, Rev. Roumaine Math. Pures Appl. 45 (2000), no. 4, 647-657.
  6. J. E. Littlewood, On inequalities in the theory of functions, Proc. London Math. Soc. (2) 23 (1925), 481-519. https://doi.org/10.1112/plms/s2-23.1.481
  7. W. Ma and D. Minda, Uniformly convex functions, Ann. Polon. Math. 57 (1992), no. 2, 165-175. https://doi.org/10.4064/ap-57-2-165-175
  8. S. Owa, On the distortion theorems. I, Kyungpook Math. J. 18 (1978), no. 1, 53-59.
  9. F. Ronnning, Uniformly convex functions and a corresponding class of starlike functions, Proc. Amer. Math. Soc. 118 (1993), no. 1, 189-196. https://doi.org/10.1090/S0002-9939-1993-1128729-7
  10. G. S. Salagean, Subclasses of univalent functions, Complex analysis|fifth Romanian-Finnish seminar, Part 1 (Bucharest, 1981), 362-372, Lecture Notes in Math., 1013, Springer, Berlin, 1983.
  11. G. S. Salagean, On some classes of univalent functions, Seminar of geometric function theory, 142-158, Preprint, 82-4, Univ. "Babes-Bolyai", Cluj-Napoca, 1983.
  12. H. M. Srivastava and S Owa, Univalent Functions, Fractional Calculus, and Their Applications, Ellis Horwood Ltd., Chichester; Halsted Press [John Wiley & Sons, Inc.], New York, 1989.