zbMATH — the first resource for mathematics

Coefficient estimates for subclass of analytic and bi-univalent functions defined by differential operator. (English) Zbl 1364.30021
Summary: In this paper, we introduce and investigate a subclass \(N^{h,p}_{\Sigma} (n, \delta, \mu, \lambda)\) of analytic and bi-univalent functions in the open unit disk \(\mathbb U\). Upper bounds for the second and third coefficients of functions in this subclass are founded. Our results, which are presented in this paper, generalize and improve those in related works of several earlier authors.

30C45 Special classes of univalent and multivalent functions of one complex variable (starlike, convex, bounded rotation, etc.)
30C50 Coefficient problems for univalent and multivalent functions of one complex variable
Full Text: DOI
[1] F. M. Al-Oboudi, On univalent functions defined by a generalized Sălăgean operator, Int. J. Math. Math. Sci. (2004) 1429-1436. · Zbl 1072.30009
[2] S. Altinkaya and S. Yalcin, Faber polynomial coefficient bounds for a subclass of bi-univalent functions, C. R. Math. Acad. Sci. Paris., 353 (2015) 1075-1080. · Zbl 1335.30005
[3] D. A. Brannan DA and T. S. Taha, On some classes of bi-univalent functions. Studia Univ Babes-Bolyai Math. 31 (1986) 70-77. · Zbl 0614.30017
[4] S. Bulut, Coefficient Estimates for New Subclasses of Analytic and Bi-Univalent Functions Defined by Al-Oboudi Differential Operator, J. Funct. Spaces Appl. (2013), Article ID 181932, 7 pages. · Zbl 1291.30065
[5] S. Bulut, Coefficient estimates for a class of analytic and biunivalent functions, Novi Sad J. Math. 43, (2013) 59-65. · Zbl 1349.30040
[6] M. Caglar, H. Orhan and N. Yagmur, Coefficient bounds for new subclasses of bi-univalent functions, Filomat 27, (2013) 1165-1171. · Zbl 1324.30017
[7] S. S. Ding, Y. Ling and G. J. Bao, Some properties of a class of analytic functions, J. Math. Anal. Appl. 195, (1995) 71-81. · Zbl 0843.30022
[8] P. L. Duren, Univalent Functions, Springer-Verlag, New York, Berlin, Heidelberg and Tokyo, 1983.
[9] B. A. Frasin and M. K. Aouf, New subclasses of bi-univalent functions, Appl. Math. Lett. 24, (2011) 1569-1573. · Zbl 1218.30024
[10] M. Lewin, On a coefficient problem for bi-univalent functions, Proc. Amer. Math. Soc. 18, (1967) 63-68. · Zbl 0158.07802
[11] E. Netanyahu, The minimal distance of the image boundary from the origin and the second coefficient of a univalent function in /z/ < 1, Arch. Rational Mech. Anal. 32, (1969) 100-112. · Zbl 0186.39703
[12] S. Porwal and M. Darus, On a new subclass of bi-univalent functions, J. Egyptian Math. Soc. 21, (2013) 190-193. · Zbl 1283.30034
[13] G. S. Sălăgean, Subclasses of univalent functions, in Complex Analysis Fifth Romanian Finish Seminar, Part 1 (Bucharest, 1981),1013 of Lecture Notes in Mathematics, 362-372, Springer, Berlin, Germany, 1983.
[14] H. M. Srivastava, A. K. Mishra and P. Gochhayat, Certain subclasses of analytic and biuniva- lent functions, Appl. Math. Lett. 23, (2010) 1188-1192. · Zbl 1201.30020
[15] H. M. Srivastava, S. Bulut, M. Caglar and N. Yagmur, Coefficient estimates for a general subclass of analytic and bi-univalent functions. Filomat 27 (2013) 831-842. · Zbl 1432.30014
[16] H. M. Srivastava and D. Bansal, Coefficient estimates for a subclass of analytic and bi-univalent functions. J. Egyptian Math. Soc. 23 (2015) 242-246. · Zbl 1326.30019
[17] H. M. Srivastava, S. Sumer Eker and R. M. Ali, Coefficient bounds for a certain class of analytic and bi-univalent functions. Filomat 29 (2015) 1839-1845. · Zbl 1458.30035
[18] H. M. Srivastava, S. B. Joshi, S. Joshi and H. Pawar, Coefficient estimates for certain subclasses of meromorphically bi-univalent functions. Palest. J. Math. 5 (Special Issue: 1) (2016) 250-258. · Zbl 1346.30011
[19] Q. H. Xu, Y. C. Gui and H. M. Srivastava, Coefficient estimates for a Certain subclass of analytic and bi-univalent functions, Appl. Math. Lett. 25, (2012) 990-994. · Zbl 1244.30033
[20] Q. H. Xu, H. G. Xiao and H. M. Srivastava, A certain general subclass of analytic and bi- univalent functions and associated coefficient estimate problems, Appl. Math. Comput. 218 (23), (2012) 11461-11465. · Zbl 1284.30009
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.