SOME PROPERTIES OF AN INTEGRAL OPERATORS DEFINED BY A NEW LINEAR OPERATOR (original) (raw)

Abstract

In this paper, we de ne a new linear operator and two new general p-valent integral operators for certain analytic functions in the unit disk . It is also shown that the rst of these operators maps Ma-Minda type starlike functions into Ma-Minda type convex functions, while the convex mapping are shown to be closed under the second integral operator.

Loading...

Loading Preview

Sorry, preview is currently unavailable. You can download the paper by clicking the button above.

References (25)

  1. J. W. Alexander, Functions which map the interior of the unit circle upon simple regions, Ann Math. 17 (1916), 12-22.
  2. D. Breaz and N. Breaz, Two integral operator, Studia Universitatis Babes- Bolyai, Mathematica, Clunj-Napoca. 3 (2002), 13-19.
  3. D. Breaz, S. Owa and S. Breaz, A new integral univalent operator, Acta Univ Apulensis Math Inf. 16 (2008), 11-16.
  4. B. C. Carlson and D. B. Shaffer, Starlike and prstarlike hypergeometric func- tions, SIAM J. Math. Anal. 15 (1984) 737-745.
  5. N. E. Cho, O. H. Kwon and H. M. Srivastava, Inclusion and argument proper- ties for certain subclasses of multivalent functions associated with a family of linear operators, J. Math. Anal. Appl. 292 (2004), 470-483.
  6. J. H. Choi, On differential subordinations of multivalent functions involving a certain fractional derivative operator, International Journal of Mathematics and Mathematical Sciences, (2010), 1-10.
  7. J. H. Choi, M. Saigo and H. M. Srivastava, Some inclusion properties of a certain family of integral opertaors, J. Math. Anal. Appl. 276 (2002), 432-445.
  8. B. A. Frasin, Convexity of integral operators of p-valent functions, Math. Com- put. Model. 51 (2010), 601-605.
  9. R. M. Goel and N. S. Sohi, A new criterion for p-valent functions, Proc. Amer. Math. Soc. 78 (1980), 353-357.
  10. Yu. E. Hohlov, Operators and operations in the class of univalent functions, Izv, Vvssh. Ucebn. Zaved. Math. 10 (1987), 83-89(in Russian)
  11. V. Kumar and S. L. Shukla, Multivalent function defined by Ruscheweyh deriva- tives, II, Indian J. Pure Appl. Math. 15 (1984), 1228-1238.
  12. J. L. Liu and Kh. I. Noor, Some properties of Noor integral operator, J. Natur. Geom. 21 (2002), 81-90.
  13. S. S. Miller, P. T. Mocanu and M. O. Read, Starlike integral operators, Pacific. J. Math. Math. Sci. 79 (1978), 157-168.
  14. J. Nishiwaki ans S. Owa, Coefficient estimates for certain analytic functions, Int. J. Math. Math. Sci., 29 (2002), 285-290.
  15. S. Owa, On certain subclass of analytic p-valent function, Math. Japan. 29 (1984), 191-198.
  16. S. Owa, On the distortion theorems, I. Kyungpook Math. J. 18 (1978), 53-59.
  17. S. Owa and J. Nishwaki, Coefficient estimates for certain classes of anaytic functions, J. Inequal. Pure Appl. Math., 3 (2002), Article 72(electronic).
  18. S. Owa and M. Srivastava, Some generalized convolution properties associated with certin subclasses of analytic functions, J. Inequal. Pure Appl. Math., 3 (2002), Article 42(electronic).
  19. S. Owa, H. M. Srivastava, Univalent starlike generalized hypergeometric func- tions, Canad. J. Math. 39 (1987), 1057-1077.
  20. Y. Polatoglu, M. Bolcal, A. S ¸en, E. Yavuz,An investigation on a subclzss of p-valently starlike functions in the unit disk, Turk. J. Math., 31 (2007), 221-228.
  21. H. Saitoh, A liner operator and its applications of first order deffrential subod- inations, Math. Japan. 44 (1996), 31-38.
  22. H. M. Srivastava and M. K. Aouf, A certain fractional derivative operator and its applications to a new class of analytic and multivalent functions with negative coefficients, I, Journal of Mathematical Analysis and Applications, 171 (1992), 1-13.
  23. H. M. Srivastava and A. A. Attiya, Some subordination results associated with certain subclasses of analytic functions, J. Inequal. Pure Appl. Math., 5 (2004), Ar- ticle 82(electronic).
  24. B. A. Uralegaddi and A. R. Desai, Convolution of univalent functions with positive coefficients, Tamkang J. Math., 29 (1998), 279-285.
  25. B. A. Uralegaddi and S. M. Sarangi, Some classes of univalent functions with negative coefficients, An. S ¸tiit ¸. Univ. Al. I. Cuza Iasi Sect. I a Mat. (N. S.) 34 (1988), 7-11 Rahim Kargar Department of Mathematics Payame Noor University Iran email: rkargar1983@gmail.com