JOURNAL BROWSE
Search
Advanced SearchSearch Tips
BI-UNIVALENT FUNCTIONS OF COMPLEX ORDER BASED ON SUBORDINATE CONDITIONS INVOLVING HURWITZ-LERCH ZETA FUNCTION
facebook(new window)  Pirnt(new window) E-mail(new window) Excel Download
 Title & Authors
BI-UNIVALENT FUNCTIONS OF COMPLEX ORDER BASED ON SUBORDINATE CONDITIONS INVOLVING HURWITZ-LERCH ZETA FUNCTION
Murugusundaramoorthy, G.; Janani, T.; Cho, Nak Eun;
  PDF(new window)
 Abstract
The purpose of the present paper is to introduce and investigate two new subclasses of bi-univalent functions of complex order defined in the open unit disk, which are associated with Hurwitz-Lerch zeta function and satisfying subordinate conditions. Furthermore, we find estimates on the Taylor-Maclaurin coefficients and for functions in the new subclasses. Several (known or new) consequences of the results are also pointed out.
 Keywords
Analytic functions;Univalent functions;Bi-univalent functions;Bi-starlike and bi-convex functions;Generalized Srivastava-Attiya operator;Hurwitz-Lerch Zeta function;
 Language
English
 Cited by
 References
1.
R. M. Ali, S.K. Lee, V. Ravichandran, S. Supramaniam, Coeffcient estimates for biunivalent Ma-Minda star-like and convex functions,Appl. Math. Lett. 25 (2012) 344-351. crossref(new window)

2.
J. W. Alexander, Functions which map the interior of the unit circle upon simple regions, Ann. Math. 17(1915), 12-22. crossref(new window)

3.
D. A. Brannan and T. S. Taha, On some classes of bi-univalent functions, Studia Univ. Babes-Bolyai Math. 31(2) (1986), 70-77.

4.
S. D. Bernardi, Convex and starlike univalent functions, Trans. Amer. Math. Soc. 135 (1969), 429-446. crossref(new window)

5.
J. Choi and H. M. Srivastava, Certain families of series associated with the Hurwitz-Lerch Zeta function, Appl. Math. Comput. 170 (2005), 399-409.

6.
E. Deniz, Certain subclasses of bi-univalent functions satisfying subordinate conditions, Jour. Class. Anal. 2(1) (2013), 49-60.

7.
C. Ferreira and J. L. Lopez, Asymptotic expansions of the Hurwitz-Lerch Zeta function, J. Math. Anal. Appl., 298 (2004), 210-224. crossref(new window)

8.
T. M. Flett, The dual of an inequality of Hardy and Littlewood and some related inequalities, J. Math. Anal. Appl. 38 (1972), 746-765 crossref(new window)

9.
B. A. Frasin and M. K. Aouf, New subclasses of bi-univalent functions, Appl. Math. Lett. 24 (2011), 1569-1573. crossref(new window)

10.
M. Garg, K. Jain and H. M. Srivastava, Some relationships between the generalized Apostol-Bernoulli polynomials and Hurwitz-Lerch Zeta functions, Integral Transform. Spec. Funct. 17 (2006), 803-815. crossref(new window)

11.
T. Hayami and S. Owa, Coeffcient bounds for bi-univalent functions, Pan Amer. Math. J. 22(4) (2012), 15-26.

12.
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. crossref(new window)

13.
R. J. Libera, Some classes of regular univalent functions, Proc. Amer. Math. Soc. 16 (1965), 755-758. crossref(new window)

14.
A. E. Livingston, On the radius of univalence of certain analytic functions, Proc. Amer. Math. Soc. 17 (1966), 352-357. crossref(new window)

15.
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.

16.
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. crossref(new window)

17.
Y. Ling and F.-S. Liu, The Choi-Saigo-Srivastava integral operator and a class of analytic functions, Appl. Math. Comput. 165 (2005), 613-621.

18.
X.-F. Li and A.-P. Wang, Two new subclasses of bi-univalent functions, Internat. Math. Forum 7 (2012), 1495-1504.

19.
W.C. Ma, D. Minda, A unified treatment of some special classes of functions, in: Proceedings of the Conference on Complex Analysis, Tianjin, 1992, 157-169, Conf. Proc. Lecture Notes Anal. 1. Int. Press, Cambridge, MA, 1994.

20.
G.Murugusundaramoorthy, Subordination results for spirallike functions associated with Hurwitz-Lerch zeta function, Integral Transform. Spec. Funct. 23(2) (2012) 97-103 crossref(new window)

21.
G. Murugusundaramoorthy , N. Magesh and V.Praemala, Coeffcient bounds for certain subclasses of bi-univalent function, Abst. Appl. Anal. 2013, Article ID 573017, 3 pages.

22.
J. K. Prajapat and S. P. Goyal, Applications of Srivastava-Attiya operator to the classes of strongly starlike and strongly convex functions, J. Math. Inequal. 3 (2009), 129-?37.

23.
C. Pommerenke, Univalent Functions, Vandenhoeck & Ruprecht, Gottingen, 1975.

24.
T. Panigarhi and G. Murugusundaramoorthy, Coeffcient bounds for Bi- univalent functions analytic functions associated with Hohlov operator, Proc. Jangjeon Math. Soc. 16 (1) (2013), 91-100.

25.
H. M. Srivastava and J. Choi, Series associated with the Zeta and related functions, Dordrecht, Boston, London: Kluwer Academic Publishers, 2001.

26.
H. M. Srivastava, A. K. Mishra and P. Gochhayat, Certain subclasses of analytic and bi-univalent functions, Appl. Math. Lett. 23 (2010), 1188-1192. crossref(new window)

27.
H. M. Srivastava, G. Murugusundaramoorthy and N. Magesh,, Certain subclasses of biunivalent functions associated with the Hohlov operator, Global Jour. Math. Anal. 1(2) (2013) 67-73.

28.
H. M. Srivastava and A. A. Attiya, An integral operator associated with the Hurwitz-Lerch Zeta function and di erential subordination, Integral Transform. Spec. Funct. 18 (2007), 207-216. crossref(new window)

29.
Q.-H. Xu, Y.-C. Gui and H. M. Srivastava, Coeffcient estimates for a certain subclass of analytic and bi-univalent functions, Appl. Math. Lett. 25 (2012), 990-994. crossref(new window)

30.
Q.-H. Xu, H.-G. Xiao and H. M. Srivastava, A certain general subclass of analytic and bi-univalent functions and associated coeffcient estimate problems, Appl. Math. Comput. 218 (2012), 11461-11465.