Kyungpook Mathematical Journal

Department of Mathematics, Kyungpook National University (경북대학교 자연과학대학 수학과)
권호 표지

On Subclasses of P-Valent Analytic Functions Defined by Integral Operators

  • Received : 2006.05.23
  • Published : 2007.09.23
Download PDF
⟨ Previous Next ⟩

Abstract

In the present paper we introduce the subclass $S^{\lambda}_{a,c}(p,A,B)$ of analytic functions and then we investigate some interesting properties of functions belonging to this subclass. Our results generalize many results known in the literature and especially generalize some of the results obtained by Ling and Liu [5].

Keywords

References

  1. V. Anh, k-fold symmetric starlike univalent functions, Bull. Austral. Math. Soc., 32(1985), 419-436. https://doi.org/10.1017/S0004972700002537
  2. N. E. Cho, O. S. Kwon, and H.M.Srivastava, Inclusion relationships and argument properties for certain subclasses of multivalent functions associated with a family of linear operators, J. Math. Anal. Appl., 292(2004), 470-483. https://doi.org/10.1016/j.jmaa.2003.12.026
  3. J. H. Choi, M. Saigo and H. M. Srivastava, Some inclusion properties of a certain integral operators, J. Math. Anal. Appl., 276(2002), 432-445. https://doi.org/10.1016/S0022-247X(02)00500-0
  4. J.-L. liu, The Noor integral operators and strongly starlike functions, J. Math. Anal. Appl., 261(2001) 441-447. https://doi.org/10.1006/jmaa.2001.7489
  5. Yi. Ling and F. Liu, The Choi-Saigo-Srivastava integral operator and a class of analytic functions, Applied Mathematics and Computations, (2004), 1-9.
  6. S. S. Miller and P. T. Mocanu, Differential Subordinations: Theory and Applications., Series in Pure and Applied Mathematics, No. 225, Marcel Dekker, New York, (2000).
  7. K. I. Noor, On new classes of integral operators, J. Natur. Geom., 238(1999), 71-80.
  8. St. Ruscheweyh, Linear operators between class of prestarlike functions, Comment. Math. Helv., 52(1977), 497-509. https://doi.org/10.1007/BF02567382
  9. St. Ruscheweyh and T. Sheil-Small, Hadamard products of schlicht functions and the Polya-Schoenberg conjecture, Comment. Math. Helv., 48(1973) 119-135. https://doi.org/10.1007/BF02566116
  10. H.Saitoh, A linear operator and its applications of first order differential subordinations, Math. Japon., 44(1996), 31-38.
  11. D. R. Wilken and J.Feng, A remark on convex and starlike functions, J. London. Math. Soc., 21(1980), 287-290. https://doi.org/10.1112/jlms/s2-21.2.287
  12. E. T. Whittaker and G. N. Watson, A Course on Modern Analysis, 4th Edition (Reprinted), Cambridge University Press, Cambridge (1927).