Neighborhoods of a certain class of analytic functions with negative coefficients
Adriana Catas
Source: Banach J. Math. Anal. Volume 3, Number 1 (2009), 111-121.
Abstract
A certain subclass of analytic functions in the open unit disc with negative coefficients is introduced. The new class is defined by means of multiplier transformations. By making use of the familiar concept of neighborhoods of analytic function, the author proves coefficient inequalities, distortion theorems and associated inclusion relations for the $(n,\delta)$-neighborhoods of functions belonging to the new class, which satisfy a certain nonhomogeneous Cauchy-Euler differential equation.
Primary Subjects: 30C45
Secondary Subjects: 30C50
Keywords: analytic function; multiplier transformation; coefficient inequality; distortion bound; inclusion relationship
Full-text: Access denied (no subscription detected)
We're sorry, but we are unable to provide you with the full text of this article because we are not able to identify you as a subscriber.
If you have a personal subscription to this journal, then please login. If you are already logged in, then you may need to update your profile to register your subscription. Read more about accessing full-text
Links and Identifiers
Permanent link to this document: http://projecteuclid.org/euclid.bjma/1240336428
Mathematical Reviews number (MathSciNet):
MR2461751
Zentralblatt MATH identifier:
05379954
References
F.M. Al-Oboudi, On univalent functions defined by a generalized Sălăgean operator, Internat. J. Math. and Math. Sci., 27 (2004), 1429--1436.
Mathematical Reviews (MathSciNet):
MR2085011
Digital Object Identifier: doi:10.1155/S0161171204108090
O. Alintaş, On a subclass of certain starlike functions with negative coefficients, Math. Japon., 36 (1991), 489--495.
Mathematical Reviews (MathSciNet):
MR1109235
Zentralblatt MATH:
0739.30011
O. Alintaş, H. Irmak, and H.M. Srivastava, Fractional calculus and certain starlike functions with negative coefficietns, Comput. Math. Appli., 30(2) (1995), 9--15.
Mathematical Reviews (MathSciNet):
MR1335761
O. Alintaş and S. Owa, Neighborhoods of certain analytic functions with negative coefficient, Internat. J. Math. and Math. Sci., 19 (1996), 797--800.
Mathematical Reviews (MathSciNet):
MR1397848
Digital Object Identifier: doi:10.1155/S016117129600110X
Zentralblatt MATH:
0915.30008
O. Alintaş, Ö. Özkan and H.M. Srivastava, Neighborhoods of class of analytic functions with negative coefficient, Appl. Math. Lett., 13, 3 (2000), 63--67.
Mathematical Reviews (MathSciNet):
MR1755745
O. Alintaş, Ö. Özkan and H.M. Srivastava, Neighborhoods of a certain family of multivalent functions with negative coefficient, Comput. Math. Appli., 47, (10)-(11) (2004), 1667--1672.
Mathematical Reviews (MathSciNet):
MR2079873
M. Acu and S. Owa, Note on a class of starlike functions, RIMS, Kyoto, 2006.
A. Cătaş, Sandwich theorems associated with new multiplier transformations, preprint.
S.K. Chatterjea, On starlike functions, J. Pure Math., 1 (1981), 23--26.
Mathematical Reviews (MathSciNet):
MR696324
N.E. Cho and H.M. Srivastava, Argument estimates of certain analytic functions defined by a class of multiplier transformations, Math. Comput. Modelling, 37 (1-2) (2003), 39--49.
Mathematical Reviews (MathSciNet):
MR1959457
Digital Object Identifier: doi:10.1016/S0895-7177(03)80004-3
Zentralblatt MATH:
1050.30007
N.E. Cho and T.H. Kim, Multiplier transformations and strongly close-to-convex functions, Bull. Korean Math. Soc., 40 (3) (2003), 399--410.
Mathematical Reviews (MathSciNet):
MR1996850
Zentralblatt MATH:
1032.30007
A.W. Goodman, Univalent functions and nonanalytic curves, Proc. Amer. Math. Soc., 8 (1957), 598--601.
Mathematical Reviews (MathSciNet):
MR86879
Digital Object Identifier: doi:10.2307/2033525
JSTOR: links.jstor.org
M.D. Hur and G.H. Oh, On certain class of analytic functions with negative coefficients, Pusan Kyongnam Math. J., 5 (1989), 69--80.
M. Kamali, Neighborhoods of a new class of p-valently functions with negative coefficients, Math. Ineq. Appl., vol.9, 4 (2006), 661--670.
Mathematical Reviews (MathSciNet):
MR2268175
Zentralblatt MATH:
1103.30005
ST. Ruscheweyh, Neighborhoods of univalent functions, Proc. Amer. Math. Soc., 81 (1981), 521--527.
Mathematical Reviews (MathSciNet):
MR601721
Digital Object Identifier: doi:10.2307/2044151
Zentralblatt MATH:
0458.30008
G.S. Sălăgean, Subclasses of univalent functions, Lecture Notes in Math., Springer Verlag, 1013(1983), 362--372.
Mathematical Reviews (MathSciNet):
MR738107
A. Schild and H. Silverman, Convolutions of univalent functions with negative coefficients, Ann. Univ. Mariae Curie-Sklodowska Sect. A., 29 (1975), 99--107.
Mathematical Reviews (MathSciNet):
MR457698
Zentralblatt MATH:
0363.30018
H. Silverman, Univalent functions with negative coefficients, Proc. Amer. Math. Soc., 51 (1975), 109--116.
Mathematical Reviews (MathSciNet):
MR369678
Digital Object Identifier: doi:10.2307/2039855
Zentralblatt MATH:
0311.30007
S. Sivaprasad Kumar, H.C. Taneja and V. Ravichandran, Classes of multivalent functions defined by Dziok-Srivastava linear operator and multiplier transformation, Kyungpook Math. J., 46 (2006), 97--109.
Mathematical Reviews (MathSciNet):
MR2214804
Zentralblatt MATH:
1104.30016
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.
Mathematical Reviews (MathSciNet):
MR904614
B.A. Uralegaddi and C. Somanatha, Certain classes of univalent functions, Current topics in analytic function theory, 371--374, World Sci. Publishing, River Edge, N.J., (1992).
Mathematical Reviews (MathSciNet):
MR1232456
Zentralblatt MATH:
0987.30508
2009 © Banach Mathematical Research Group
Banach Journal of Mathematical Analysis
