Meromorphic parabolic starlike functions with a fixed point involving Srivastava-Attiya operator
Downloads
DOI:
https://doi.org/10.26637/mjm202/001Abstract
In the present investigation, we introduce a new class of meromorphic parabolic starlike functions with a fixed point defined in the punctured unit disk \(\Delta^*:=\{z \in \mathbb{C}: 0<|z|<1\}\) by making use of the SrivastavaAttiya Operator \(\mathcal{J}_b^s\). We obtained Coefficient inequalities, growth and distortion inequalities, as well as closure results for functions \(f \in \mathcal{M}_b^s(\lambda, \beta, \gamma)\). We further established some results concerning convolution and the partial sums.
Keywords:
Meromorphic functions, starlike function, convolution, positive coefficients, coefficient inequalities, integral operatorMathematics Subject Classification:
30C50- Pages: 91-102
- Date Published: 01-04-2014
- Vol. 2 No. 02 (2014): Malaya Journal of Matematik (MJM)
J. W. Alexander, Functions which map the interior of the unit circle upon simple regions, Ann. Math.Ser.2, 17(1915), 12–22. DOI: https://doi.org/10.2307/2007212
M. K. Aouf, On a certain class of meromorphic univalent functions with positive coefficients, Rend. Mat.Appl. 7(11)(2)(1991), 209-219.
M.K.Aouf and G.Murugusundaramoorthy, A subclass of uniformly convex functions defined by the Dziok-Srivastava operator, Aust.J. Math. Anal. Appln., 5(1)(2008), 1–17.
S.D. Bernardi, Convex and starlike univalent functions, Trans. Amer. Math. Soc., 135(1969), 429–446. DOI: https://doi.org/10.1090/S0002-9947-1969-0232920-2
J.Choi and H. M. Srivastava, Certain families of series associated with the Hurwitz-Lerch Zeta function, Appl. Math. Comput.,170(2005), 399-409. DOI: https://doi.org/10.1016/j.amc.2004.12.004
N.E.Cho and S.Owa, Partial sums of certain meromorphic functions , JIPAM, 5(2)(2004), 1-10.
J.Dziok, G.Murugusundaramoorthy, and J. Sokół, On certain class of meromorphic functions with positive coefficients, Acta Mathematica Scientia, 32B(4)(2012), 1–16. DOI: https://doi.org/10.1016/S0252-9602(12)60106-4
A.W.Goodman,On uniformly starlike functions, J. Math. Anal. Appl., 155(1991),364–370. DOI: https://doi.org/10.1016/0022-247X(91)90006-L
A.W.Goodman,On uniformly convex functions, Ann. Polon. Math., 56(1)(1991), 87–92. DOI: https://doi.org/10.4064/ap-56-1-87-92
I.B.Jung,Y.C.Kim and H. M. Srivastava, The Hardy space of analytic functions associated with certain one-parameter families of integral operators, J. Math. Anal. Appl., 176(1993), 138-147. DOI: https://doi.org/10.1006/jmaa.1993.1204
S. Kanas and F. Ronning, Uniformaly starlike and convex function and other related classes of univalent functions, Ann. Univ. Marie Curie-Sklodowaska, A53(1991), 95–105.
S.-D. Lin and H. M. Srivastava, Some families of the Hurwitz-Lerch Zeta functions and associated fractional derivative and other integral representations, Appl. Math. Comput., 154(2004), 725-733. DOI: https://doi.org/10.1016/S0096-3003(03)00746-X
S.-D. Lin, H. M. Srivastava and P.-Y. Wang, Some espansion formulas for a class of generalized Hurwitz-Lerch Zeta functions, Integral Transform. Spec. Funct.,17(2006), 817-827. DOI: https://doi.org/10.1080/10652460600926923
R. J. Libera, Some classes of regular univalent functions, Proc. Amer. Math. Soc., 16(1969), 755–758. DOI: https://doi.org/10.1090/S0002-9939-1965-0178131-2
J. -L. Liu, Properties of some families of meromorphic p-valent functions, Math. Japon. 52(3)(2000), 425-434.
J-L. Liu,Some inclusion properties for certain subclass of meromorphically multivalent functions involving the Srivastava-Attiya operator,Tamsui Oxford Journal of Information and Mathematical Sciences, 28(3)(2012) 267–279.
J.-L. Liu and H.M. Srivastava, Classes of meromorphically multivalent functions associated with the generalized hypergeometric function, Math. Comput. Modelling, 39(2004), 21-34. DOI: https://doi.org/10.1016/S0895-7177(04)90503-1
J.-L. Liu and H.M. Srivastava, Subclasses of meromorphically multivalent functions associated with a certain linear operator, Math. Comput.Modelling, 39 (2004) 35-44. DOI: https://doi.org/10.1016/S0895-7177(04)90504-3
M. L. Mogra, T. R. Reddy and O. P. Juneja,Meromorphic univalent functions with positive coefficients, Bull.Austral. Math. Soc., 32(1985), 161–176. DOI: https://doi.org/10.1017/S0004972700009874
S. Owa and N. Pascu, Coefficient inequalities for certain classes of meromorphically starlike and meromorphically convex functions, J. Inequal. Pure Appl. Math., 4(1)(2003), 1-6.
Ch. Pommerenke, On meromorphic starlike functions, Pacific J. Math., 13(1963), 221-235. DOI: https://doi.org/10.2140/pjm.1963.13.221
H. Silverman, Partial sums of starlike and convex functions, J.Math. Anal. Appl., 209(1997), 221 - 227. DOI: https://doi.org/10.1006/jmaa.1997.5361
H. M. Srivastava and A. A. Attiya, An integral operator associated with the Hurwitz-Lerch Zeta function and differential subordination, Integral Transform. Spec. Funct., 18(2007), 207–216. DOI: https://doi.org/10.1080/10652460701208577
H.M. Srivastava and J.Choi, Series associated with the Zeta and related functions (Kluwer Academic Publishers, Dordrecht, Boston, London, 2001). DOI: https://doi.org/10.1007/978-94-015-9672-5
B. A.Uralegaddi and C. Somanatha, Certain differential operators for meromorphic functions, Houston J. Math., 17(2)(1991), 279-284.
- NA
Similar Articles
- Naima Ablaoui-Lahmar, Omar Belhamiti, Sidi Mohammed Bahri, A new Legendre wavelets decomposition method for solving PDEs , Malaya Journal of Matematik: Vol. 2 No. 01 (2014): Malaya Journal of Matematik (MJM)
You may also start an advanced similarity search for this article.
Metrics
Published
How to Cite
Issue
Section
License
Copyright (c) 2014 MJM
This work is licensed under a Creative Commons Attribution 4.0 International License.
