Geodesic
Inclusion and neighborhood properties of certain subclasses of p-valent functions of complex order defined by convolution
Annales Universitatis Mariae Curie-Skłodowska. Mathematica , Tome 65 (2011) no. 1.

Voir la notice de l'article provenant de la source Library of Science

In this paper we introduce and investigate three new subclasses of p-valent analytic functions by using the linear operator D_λ,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,θ)-neighborhoods of subclasses of analytic and multivalent functions with negative coefficients, which are defined by means of a non-homogenous differential equation.
Keywords: Analytic, \(p\)-valent, \((n,\theta)\)-neighborhood, inclusion relations 
@article{AUM_2011_65_1_a1,
     author = {El-Ashwah, R. M. and Aouf, M. K. and El-Deeb, S. M.},
     title = {Inclusion and neighborhood properties of certain subclasses of p-valent functions of complex order defined by convolution},
     journal = {Annales Universitatis Mariae Curie-Sk{\l}odowska. Mathematica },
     publisher = {mathdoc},
     volume = {65},
     number = {1},
     year = {2011},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/AUM_2011_65_1_a1/}
}
TY  - JOUR
AU  - El-Ashwah, R. M.
AU  - Aouf, M. K.
AU  - El-Deeb, S. M.
TI  - Inclusion and neighborhood properties of certain subclasses of p-valent functions of complex order defined by convolution
JO  - Annales Universitatis Mariae Curie-Skłodowska. Mathematica 
PY  - 2011
VL  - 65
IS  - 1
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/AUM_2011_65_1_a1/
LA  - en
ID  - AUM_2011_65_1_a1
ER  - 
%0 Journal Article
%A El-Ashwah, R. M.
%A Aouf, M. K.
%A El-Deeb, S. M.
%T Inclusion and neighborhood properties of certain subclasses of p-valent functions of complex order defined by convolution
%J Annales Universitatis Mariae Curie-Skłodowska. Mathematica 
%D 2011
%V 65
%N 1
%I mathdoc
%U http://geodesic.mathdoc.fr/item/AUM_2011_65_1_a1/
%G en
%F AUM_2011_65_1_a1
El-Ashwah, R. M.; Aouf, M. K.; El-Deeb, S. M. Inclusion and neighborhood properties of certain subclasses of p-valent functions of complex order defined by convolution. Annales Universitatis Mariae Curie-Skłodowska. Mathematica , Tome 65 (2011) no. 1. http://geodesic.mathdoc.fr/item/AUM_2011_65_1_a1/

[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).