DOI QR코드

DOI QR Code

ON SANDWICH THEOREMS FOR CERTAIN SUBCLASSES OF ANALYTIC FUNCTIONS INVOLVING CARLSON-SHAFFER OPERATOR

  • Shanmugam, Tirunelveli Nellaiappan ;
  • Srikandan, Sivasubramanian ;
  • Frasin, Basem Aref ;
  • Kavitha, Seetharaman
  • Published : 2008.05.31

Abstract

The purpose of this present paper is to derive some subordination and superordination results involving Carlson-Shaffer operator for certain normalized analytic functions in the open unit disk. Relevant connections of the results, which are presented in the paper, with various known results are also considered.

Keywords

differential subordinations;differential superordinations;dominant;subordinant

References

  1. R. M. Ali, V. Ravichandran, M. Hussain Khan, and K. G. Subramanian, Differential sandwich theorems for certain analytic functions, Far East J. Math. Sci. (FJMS) 15 (2005), no. 1, 87-94
  2. T. Bulboaca, A class of superordination-preserving integral operators, Indag. Math., New Ser. 13 (2002), no. 3, 301-311 https://doi.org/10.1016/S0019-3577(02)80013-1
  3. B. C. Carlson and D. B. Shaffer, Starlike and prestarlike hypergeometric functions, SIAM J. Math. Anal. 15 (1984), no. 4, 737-745 https://doi.org/10.1137/0515057
  4. S. S. Miller and P. T. Mocanu, Differential Subordinations: Theory and Applications, Pure and Applied Mathematics No. 225, Marcel Dekker, New York, 2000
  5. S. S. Miller and P. T. Mocanu, Subordinants of differential superordinations, Complex Variables 48 (2003), no. 10, 815-826 https://doi.org/10.1080/02781070310001599322
  6. M. Obradovic, A class of univalent functions, Hokkaido Math. J. 27 (1998), no. 2, 329-335 https://doi.org/10.14492/hokmj/1351001289
  7. S. Ruscheweyh, New criteria for univalent functions, Proc. Amer. Math. Soc. 49 (1975), 109-115 https://doi.org/10.2307/2039801
  8. H. M. Srivastava and A. Y. Lashin, Some applications of the Briot-Bouquet differential subordination, J. Inequal. Pure Appl. Math. 6 (2005), no. 2, Article 41, 7 pp
  9. N. Tuneski, On certain sufficient conditions for starlikeness, Internat J. Math. Math. Sci. 23 (2000), no. 8, 521-527 https://doi.org/10.1155/S0161171200003574
  10. N. Tuneski and M. Darus, Fekete-Szego functional for non-Bazilevic functions, Acta Mathematica Academia Paedagogicae Nyiregyhaziensis 18 (2002), 63-65
  11. Z. Wang, C. Gao, and M. Liao, On certain generalized class of non-Bazilevic functions, Acta Mathematica Academia Paedagogicae Nyiregyhaziensis 21 (2005), 147-154
  12. T. N. Shanmugam, V. Ravichandran, and S. Sivasubramanian, Differential sandwich theorems for some subclasses of analytic functions, to appear in Aust. J. Math. Anal. Appl

Cited by

  1. Some Subclasses of Meromorphic Functions Associated with a Family of Integral Operators vol.2009, pp.1, 2009, https://doi.org/10.1155/2009/931230
  2. Differential sandwich results for certain subclasses of analytic functions vol.54, pp.1-2, 2011, https://doi.org/10.1016/j.mcm.2011.03.028
  3. Convolution operators in the geometric function theory vol.2012, pp.1, 2012, https://doi.org/10.1186/1029-242X-2012-213
  4. On certain differential sandwich theorems involving a generalized Sǎlǎgean operator and Ruscheweyh operator vol.23, pp.1, 2015, https://doi.org/10.1515/auom-2015-0003
  5. Sandwich Theorems for Certain Subclasses of Analytic Functions Defined by Family of Linear Operators vol.15, pp.2, 2009, https://doi.org/10.1515/JAA.2009.269
  6. Subordination and superordination results for the family of Jung-Kim-Srivastava integral operators vol.24, pp.1, 2010, https://doi.org/10.2298/FIL1001069S
  7. Sufficient Conditions for Non-Bazilevič Functions vol.2013, 2013, https://doi.org/10.1155/2013/154912