NEIGHBORHOODS OF CERTAIN SUBCLASSES OF ANALYTIC FUNCTIONS WITH NEGATIVE COEFFICIENTS

Title & Authors
NEIGHBORHOODS OF CERTAIN SUBCLASSES OF ANALYTIC FUNCTIONS WITH NEGATIVE COEFFICIENTS
Darwish, Hanan E.; Aouf, Mohamed K.;

Abstract
The main object of this paper is to prove several inclusion relations associated with (j, $\small{{\delta}}$)-neighborhoods of various subclasses defined by Salagean operator by making use of the familiar concept of neighborhoods of analytic functions. Special cases of some of these inclusion relations are shown to yield known results.
Keywords
analytic functions;(j, $\small{{\delta}}$)-neighborhood;Salagean operator;complex order;
Language
English
Cited by
References
1.
O. Altintas and S. Owa, Neighborhoods of certain analytic functions with negative coefficients, Internat. J. Math. Math. Sci. 19 (1996), no. 4, 797-800.

2.
O. Altintas, O. Ozkan, and H. M. Srivastava, Neighborhoods of a class of analytic functions with negative coefficients, Appl. Math. Lett. 13 (2000), no. 3, 63-67.

3.
M. K. Aouf, Neighborhoods of certain classes of analytic functions with negative coefficients, Int. J. Math. Math. Sci. 2006 (2006), Art. ID 38258, 6 pp.

4.
M. K. Aouf, H. E. Darwish, and A. A. Attiya, Generalization of certain subclasses of analytic functions with negative coefficients, Studia Univ. Babes-Bolyai Math. 45 (2000), no. 1, 11-22.

5.
M. K. Aouf, H. M. Hossen, and A. Y. Lashin, On certain families of analytic functions with negative coefficients, Indian J. Pure Appl. Math. 31 (2000), no. 8, 999-1015.

6.
S. K. Chatterjea, On starlike functions, J. Pure Math. 1 (1981), 23-26.

7.
A. W. Goodman, Univalent functions and nonanalytic curves, Proc. Amer. Math. Soc. 8 (1957), 598-601.

8.
H. M. Hossen, G. S. Salagean, and M. K. Aouf, Notes on certain classes of analytic functions with negative coefficients, Mathematica 39(62) (1997), no. 2, 165-179.

9.
H. Orhan and M. Kamali, Neighborhoods of a class of analytic functions with negative coefficients, Acta Math. Acad. Paedagog. Nyhazi. (N.S.) 21 (2005), no. 1, 55-61.

10.
St. Ruscheweyh, Neighborhoods of univalent functions, Proc. Amer. Math. Soc. 81 (1981), no. 4, 521-527.

11.
G. S. Salagean, Subclasses of univalent functions, Complex analysis-fifth Romanian-Finnish seminar, Part 1 (Bucharest, 1981), 362-372, Lecture Notes in Math., 1013, Springer, Berlin, 1983.

12.
T. Sekine, Generalization of certain subclasses of analytic functions, Internat. J. Math. Math. Sci. 10 (1987), no. 4, 725-732.

13.
H. M. Srivastava, S. Owa, and S. K. Chatterjea, A note on certain classes of starlike functions, Rend. Sem. Mat. Univ. Padova 77 (1987), 115-124.