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ArticleOriginal scientific text

Title

Inclusion and neighborhood properties of certain subclasses of p-valent functions of complex order defined by convolution

Authors , ,

Abstract

In this paper we introduce and investigate three new subclasses of p-valent analytic functions by using the linear operator Dλ,pm(f∗g)(z). The various results obtained here for each of these function classes include coefficient bounds, distortion inequalities and associated inclusion relations for (n,θ)-neighborhoods of subclasses of analytic and multivalent functions with negative coefficients, which are defined by means of a non-homogenous differential equation.

Keywords

ENG
Analytic, p-valent, (n,θ)-neighborhood, inclusion relations

Bibliography

  1. Altintas, O., Neighborhoods of certain p-valently analytic functions with negative coefficients, Appl. Math. Comput. 187 (2007), 47-53.
  2. Altintas, O., Irmak, H. and Srivastava, H. M., Neighborhoods for certain subclasses of multivalently analytic functions defined by using a differential operator, Comput. Math. Appl. 55 (2008), 331-338.
  3. Altintas, O., Ozkan, O. and Srivastava, H. M., Neighborhoods of a certain family of multivalent functions with negative coefficient, Comput. Math. Appl. 47 (2004), 1667-1672.
  4. Aouf, M. K., Inclusion and neighborhood properties for certain subclasses of analytic functions associated with convolution structure, J. Austral. Math. Anal. Appl. 6, no. 2 (2009), Art. 4, 1-10.
  5. Aouf, M. K., Mostafa, A. O., On a subclass of n-p-valent prestarlike functions, Comput. Math. Appl. 55 (2008), 851-861.
  6. Aouf, M. K., Seoudy, T. M., On differential sandwich theorems of analytic functions defined by certain linear operator, Ann. Univ. Marie Curie-Skłodowska Sect. A, 64 (2) (2010), 1-14.
  7. Catas, A., On certain classes of p-valent functions defined by multiplier transformations, Proceedings of the International Symposium on Geometric Function Theory and Applications: GFTA 2007 Proceedings (Istanbul, Turkey; 20-24 August 2007) (S. Owa and Y. Polato¸glu, Editors), pp. 241-250, TC Istanbul Kultur University Publications, Vol. 91, TC Istanbul Kultur University, ˙Istanbul, Turkey, 2008.
  8. El-Ashwah, R. M., Aouf, M. K., Inclusion and neighborhood properties of some analytic p-valent functions, General Math. 18, no. 2 (2010), 173-184.
  9. Frasin, B. A., Neighborhoods of certain multivalent analytic functions with negative coefficients, Appl. Math. Comput. 193, no. 1 (2007), 1-6.
  10. Goodman, A. W., Univalent functions and non-analytic curves, Proc. Amer. Math. Soc. 8 (1957), 598-601.
  11. Kamali, M., Orhan, H., On a subclass of certain starlike functions with negative coefficients, Bull. Korean Math. Soc. 41, no. 1 (2004), 53-71.
  12. Mahzoon, H., Latha, S., Neighborhoods of multivalent functions, Internat. J. Math. Analysis, 3, no. 30 (2009), 1501-1507.
  13. Orhan, H., Kiziltunc, H., A generalization on subfamily of p-valent functions with negative coefficients, Appl. Math. Comput. 155 (2004), 521-530.
  14. Prajapat, J. K., Raina, R. K. and Srivastava, H. M., Inclusion and neighborhood properties of certain classes of multivalently analytic functions associated with convolution structure, JIPAM. J. Inequal. Pure Appl. Math. 8, no. 1 (2007), Article 7, 8 pp. (electronic).
  15. Raina, R. K., Srivastava, H. M., Inclusion and neighborhood properties of some analytic and multivalent functions, J. Inequal. Pure Appl. Math. 7, no. 1 (2006), 1-6.
  16. Ruscheweyh, St., Neighborhoods of univalent functions, Proc. Amer. Math. Soc. 81 (1981), 521-527.
  17. Srivastava, H. M., Orhan, H., Coefficient inequalities and inclusion relations for some families of analytic and multivalent functions, Applied Math. Letters, 20, no. 6 (2007), 686-691.
  18. Srivastava, H. M., Suchithra, K., Stephen, B. A. and Sivasubramanian, S., Inclusion and neighborhood properties of certain subclasses of analytic and multivalent functions of complex order, JIPAM. J. Inequal. Pure Appl. Math. 7, no. 5 (2006), Article 191, 8 pp. (electronic).
Annales Universitatis Mariae Curie-Skłodowska, sectio A – Mathematica
2011/65/1
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Main language of publication
English
Published
2011
Published online
2016-07-25

DOI: 10.17951/a.2011.65.1.33-48

Exact and natural sciences