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

R. M. El-Ashwah ; M. K. Aouf ; S. M. El-Deeb

Annales Universitatis Mariae Curie-Skłodowska, sectio A – Mathematica, Tome 65 (2011), / Harvested from The Polish Digital Mathematics Library

Résumé

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

Détail

Publié le : 2011-01-01
EUDML-ID : urn:eudml:doc:289762

Bibliographie

Altintas, O., Neighborhoods of certain p-valently analytic functions with negative coefficients, Appl. Math. Comput. 187 (2007), 47-53.

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.

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.

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.

Aouf, M. K., Mostafa, A. O., On a subclass of n-p-valent prestarlike functions, Comput. Math. Appl. 55 (2008), 851-861.

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.

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.

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.

Frasin, B. A., Neighborhoods of certain multivalent analytic functions with negative coefficients, Appl. Math. Comput. 193, no. 1 (2007), 1-6.

Goodman, A. W., Univalent functions and non-analytic curves, Proc. Amer. Math. Soc. 8 (1957), 598-601.

Kamali, M., Orhan, H., On a subclass of certain starlike functions with negative coefficients, Bull. Korean Math. Soc. 41, no. 1 (2004), 53-71.

Mahzoon, H., Latha, S., Neighborhoods of multivalent functions, Internat. J. Math. Analysis, 3, no. 30 (2009), 1501-1507.

Orhan, H., Kiziltunc, H., A generalization on subfamily of p-valent functions with negative coefficients, Appl. Math. Comput. 155 (2004), 521-530.

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).

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.

Ruscheweyh, St., Neighborhoods of univalent functions, Proc. Amer. Math. Soc. 81 (1981), 521-527.

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.

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).