Coefficient Estimates for a Certain General Subclass of Analytic and Bi-Univalent Functions

Affiliation(s)

Post-Graduate and Research Department of Mathematics, Government Arts College for Men, Krishnagiri, India.

Department of Mathematics, Govt First Grade College, Bangalore, India.

Post-Graduate and Research Department of Mathematics, Government Arts College for Men, Krishnagiri, India.

Department of Mathematics, Govt First Grade College, Bangalore, India.

ABSTRACT

Motivated and stimulated especially by the work of Xu et al. [1], in this paper, we introduce and discuss an interesting subclass of analytic and bi-univalent functions defined in the open unit disc U. Further, we find estimates on the coefficients and for functions in this subclass. Many relevant connections with known or new results are pointed out.

Cite this paper

Magesh, N. and Yamini, J. (2014) Coefficient Estimates for a Certain General Subclass of Analytic and Bi-Univalent Functions.*Applied Mathematics*, **5**, 1047-1052. doi: 10.4236/am.2014.57098.

Magesh, N. and Yamini, J. (2014) Coefficient Estimates for a Certain General Subclass of Analytic and Bi-Univalent Functions.

References

[1] Xu, Q.-H., Gui, Y.-C. and Srivastava, H.M. (2012) Coefficient Estimates for a Certain Subclass of Analytic and Bi-Univalent Functions. Applied Mathematics Letters, 25, 990-994.

[2] Srivastava, H.M., Mishra, A.K. and Gochhayat, P. (2010) Certain Subclasses of Analytic and Bi-Univalent Functions. Applied Mathematics Letters, 23, 1188-1192.

[3] Ali, R.M., Lee, S.K., Ravichandran, V. and Supramanian, S. (2012) Coefficient Estimates for Bi-Univalent Ma-Minda Starlike and Convex Functions. Applied Mathematics Letters, 25, 344-351.

[4] Bulut, S. (2013) Coefficient Estimates for a Class of Analytic and Bi-Univalent Functions. Novi Sad Journal of Mathematics, 43, 59-65.

[5] Caglar, M., Orhan, H. and Yagmur, N. (2012) Coefficient Bounds for New Subclasses of Bi-Univalent Functions. FILOMAT, 27, 1165-1171.

[6] Frasin, B.A. and Aouf, M.K. (2011) New Subclasses of Bi-Univalent Functions. Applied Mathematics Letters, 24, 1569-1573.

[7] Hayami, T. and Owa, S. (2012) Coefficient Bounds for Bi-Univalent Functions. Pan American Mathematical Journal, 22, 15-26.

[8] Li, X.-F. and Wang, A.-P. (2012) Two New Subclasses of Bi-Univalent Functions. International Mathematical Forum, 7, 1495-1504.

[9] Magesh, N., Rosy, T. and Varma, S. (2013) Coefficient Estimate Problem for a New Subclass of Biunivalent Functions. Journal of Complex Analysis, 2013, Article ID: 474231, 3 Pages.

[10] Murugusundaramoorthy, G., Magesh, N. and Prameela, V. (2013) Coefficient Bounds for Certain Subclasses of Bi-Univalent Functions. Abstract and Applied Analysis, 2013, Article ID: 573017, 3 Pages.

[11] Srivastava, H.M., Bulut, S., CaGlar, M. and Yagmur, N. (2013) Coefficient Estimates for a General Subclass of Analytic and Bi-Univalent Functions. FILOMAT, 27, 831-842.

[12] Srivastava, H.M., Murugusundaramoorthy, G. and Magesh, N. (2013) On Certain Subclasses of Bi-Univalent Functions Associated with Hohlov Operator. Global J. Math. Anal, 1, 67-73.

[13] Xu, Q.-H., Xiao, H.-G. and Srivastava, H. M. (2012) A Certain General Subclass of Analytic and Bi-Univalent Functions and Associated Coefficient Estimate Problems. Applied Mathematics and Computation, 218, 11461-11465.

[14] Brannan, D.A. and Taha, T.S. (1986) On Some Classes of Bi-Univalent Functions. Studia Universitatis Babes-Bolyai. Mathematica, 31, 70-77.

[1] Xu, Q.-H., Gui, Y.-C. and Srivastava, H.M. (2012) Coefficient Estimates for a Certain Subclass of Analytic and Bi-Univalent Functions. Applied Mathematics Letters, 25, 990-994.

[2] Srivastava, H.M., Mishra, A.K. and Gochhayat, P. (2010) Certain Subclasses of Analytic and Bi-Univalent Functions. Applied Mathematics Letters, 23, 1188-1192.

[3] Ali, R.M., Lee, S.K., Ravichandran, V. and Supramanian, S. (2012) Coefficient Estimates for Bi-Univalent Ma-Minda Starlike and Convex Functions. Applied Mathematics Letters, 25, 344-351.

[4] Bulut, S. (2013) Coefficient Estimates for a Class of Analytic and Bi-Univalent Functions. Novi Sad Journal of Mathematics, 43, 59-65.

[5] Caglar, M., Orhan, H. and Yagmur, N. (2012) Coefficient Bounds for New Subclasses of Bi-Univalent Functions. FILOMAT, 27, 1165-1171.

[6] Frasin, B.A. and Aouf, M.K. (2011) New Subclasses of Bi-Univalent Functions. Applied Mathematics Letters, 24, 1569-1573.

[7] Hayami, T. and Owa, S. (2012) Coefficient Bounds for Bi-Univalent Functions. Pan American Mathematical Journal, 22, 15-26.

[8] Li, X.-F. and Wang, A.-P. (2012) Two New Subclasses of Bi-Univalent Functions. International Mathematical Forum, 7, 1495-1504.

[9] Magesh, N., Rosy, T. and Varma, S. (2013) Coefficient Estimate Problem for a New Subclass of Biunivalent Functions. Journal of Complex Analysis, 2013, Article ID: 474231, 3 Pages.

[10] Murugusundaramoorthy, G., Magesh, N. and Prameela, V. (2013) Coefficient Bounds for Certain Subclasses of Bi-Univalent Functions. Abstract and Applied Analysis, 2013, Article ID: 573017, 3 Pages.

[11] Srivastava, H.M., Bulut, S., CaGlar, M. and Yagmur, N. (2013) Coefficient Estimates for a General Subclass of Analytic and Bi-Univalent Functions. FILOMAT, 27, 831-842.

[12] Srivastava, H.M., Murugusundaramoorthy, G. and Magesh, N. (2013) On Certain Subclasses of Bi-Univalent Functions Associated with Hohlov Operator. Global J. Math. Anal, 1, 67-73.

[13] Xu, Q.-H., Xiao, H.-G. and Srivastava, H. M. (2012) A Certain General Subclass of Analytic and Bi-Univalent Functions and Associated Coefficient Estimate Problems. Applied Mathematics and Computation, 218, 11461-11465.

[14] Brannan, D.A. and Taha, T.S. (1986) On Some Classes of Bi-Univalent Functions. Studia Universitatis Babes-Bolyai. Mathematica, 31, 70-77.