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BY-NC-ND 3.0 license Open Access Published by De Gruyter March 6, 2014

Majorization properties for a new subclass of θ-spiral functions of order γ

  • Huo Tang EMAIL logo , Shu-hai Li and Guan-tie Deng
From the journal Mathematica Slovaca

Abstract

In the present paper, we introduce a new subclass S p,q,s,λm,l(γ, θ) of θ-spiral functions of order γ defined by a class of generalized multiplier transformations. Majorization properties for functions belonging to the class S p,q,s,λm,l(γ, θ) are considered. Moreover, we point out some new or known consequences of our main result.

[1] MACGREGOR, T. H.: Majorization by univalent functions, Duke Math. J. 34 (1967), 95–102. http://dx.doi.org/10.1215/S0012-7094-67-03411-410.1215/S0012-7094-67-03411-4Search in Google Scholar

[2] SRIVASTAVA, H. M.— KARLSSON, P. W.: Multiple Gaussion Hypergeometric Series, Halsted Press, Ellis Horwood Limited/John Wiley and Sons, Chichester/New York-Chichester-Brisbane-Toronto, 1985. Search in Google Scholar

[3] SELVARAJ, C.— KARTHIKEYAN, K. R.: Differential subordination and superordinations for certain subclasses of analytic functions, Far East J. Math. Sci. (FJMS) 29 (2008), 419–430. Search in Google Scholar

[4] DZIOK, J.— SRIVASTAVA, H. M.: Classes of analytic functions associated with the generalized hypergeometric function, Appl. Math. Comput. 103 (1999), 1–13. http://dx.doi.org/10.1016/S0096-3003(98)10042-510.1016/S0096-3003(98)10042-5Search in Google Scholar

[5] DZIOK, J.— SRIVASTAVA, H. M.: Certain subclasses of analytic functions associated with the generalized hypergeometric function, Integral Transforms Spec. Funct. 14 (2003), 7–18. http://dx.doi.org/10.1080/1065246030454310.1080/10652460304543Search in Google Scholar

[6] CATAS, A.: On certain classes of p-valent functions defined by multiplier transformations. In: Proc. Book of the International Symposium on Geometric Function Theory and Applications, Istanbul, Turkey, August 2007, pp. 241–250. Search in Google Scholar

[7] KUMAR, S. S.— TANEJA, H. C.— RAVICHANDRAN, V.: Classes multivalent functions defined by Dziok-Srivastava linear operator and multiplier transformations, Kyungpook Math. J. 46 (2006), 97–109. Search in Google Scholar

[8] KAMALI, M.— ORHAN, H.: On a subclass of certain starlike functions with negative coefficients, Bull. Korean Math. Soc. 41 (2004), 53–71. http://dx.doi.org/10.4134/BKMS.2004.41.1.05310.4134/BKMS.2004.41.1.053Search in Google Scholar

[9] AOUF, M. K.— MOSTAFA, A. O.: On a subclass of n — p-valent prestarlike functions, Comput. Math. Appl. 55 (2008), 851–861. http://dx.doi.org/10.1016/j.camwa.2007.05.01010.1016/j.camwa.2007.05.010Search in Google Scholar

[10] CHO, N. E.— SRIVASTAVA, H. M.: Argument estimates of certain analytic functions defined by a class of multiplier transformations, Math. Comput. Modelling 37 (2003), 39–49. http://dx.doi.org/10.1016/S0895-7177(03)80004-310.1016/S0895-7177(03)80004-3Search in Google Scholar

[11] CHO, N. E.— KIM, T. H.: Multiplier transformations and strongly close-to-convex functions, Bull. Korean Math. Soc. 40 (2003), 399–410. http://dx.doi.org/10.4134/BKMS.2003.40.3.39910.4134/BKMS.2003.40.3.399Search in Google Scholar

[12] Al-Oboudi, F. M.: On univalent functions defined by a generalized Salagean operator, Internat. J. Math. Math. Sci. 27 (2004), 1429–1436. http://dx.doi.org/10.1155/S016117120410809010.1155/S0161171204108090Search in Google Scholar

[13] SALAGEAN, G. S.: Subclasses of univalent functions. In: Lecture Notes in Math. 1013, Springer-Verlag, New York, 1983, pp. 362–372. Search in Google Scholar

[14] LIBERA, R. J.: Univalent α-spiral functions, Canadian. J. Math. 19 (1967), 449–456. http://dx.doi.org/10.4153/CJM-1967-038-010.4153/CJM-1967-038-0Search in Google Scholar

[15] ROBERTSON, M. I. S.: On the theory of univalent functions, Ann. Math. 37 (1936), 374–408. http://dx.doi.org/10.2307/196845110.2307/1968451Search in Google Scholar

[16] SPACEK, L.: Contribution a la théorie des fonctions univalentes, Časopis Pěst. Mat. 662 (1932), 12–19 (Russian). Search in Google Scholar

[17] ALTINTAS, O.— OZKAN, O.— SRIVASTAVA, H. M.: Majorization by starlike functions of complex order, Complex Variables Theory Appl. 46 (2001), 207–218. http://dx.doi.org/10.1080/1747693010881540910.1080/17476930108815409Search in Google Scholar

[18] GOYAL, S. P.— GOSWAMI, P.: Majorization for certain classes of analytic functions defined by fractional derivatives, Appl. Math. Lett. 22 (2009), 1855–1858. http://dx.doi.org/10.1016/j.aml.2009.07.00910.1016/j.aml.2009.07.009Search in Google Scholar

[19] GOYAL, S. P.— BANSAL, S. K.— GOSWAMI, P.: Majorization for subclass of analytic functions defined by linear operator using differential subordination, J. Appl. Math. Stat. Inform. 6 (2010), 45–50. Search in Google Scholar

[20] GOSWAMI, P.— AOUF, M. K.: Majorization properties for certain classes of analytic functions using the Salagean operator, Appl. Math. Lett. 23 (2010), 1351–1354. http://dx.doi.org/10.1016/j.aml.2010.06.03010.1016/j.aml.2010.06.030Search in Google Scholar

[21] GOSWAMI, P.— SHARMA, B.— BULBOACA, T.: Majorization for certain classes of analytic functions using multiplier transformation, Appl. Math. Lett. 23 (2010), 633–637. http://dx.doi.org/10.1016/j.aml.2010.01.02910.1016/j.aml.2010.01.029Search in Google Scholar

[22] NEHARI, Z.: Conformal mapping, MacGraw-Hill Book Company, New York-Toronto-London, 1955. Search in Google Scholar

Published Online: 2014-3-6
Published in Print: 2014-2-1

© 2014 Mathematical Institute, Slovak Academy of Sciences

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.

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