A Certain Subclass of Analytic Functions with Bounded Positive Real Part

ABSTRACT

For real numbers *α* and *β* such that 0≤*α*＜1＜*β*, we denote by *T*(*α*,*β*) the class of normalized analytic functions which satisfy , where U denotes the open unit disk. We find some relationships involving functions in the class *T*(*α*,*β*). And we estimate the bounds of coefficients and solve Fekete-Szego problem for functions in this class. Furthermore, we investigate the bounds of initial coefficients of inverse functions or bi-univalent functions.

Cite this paper

Y. Sim and O. Kwon, "A Certain Subclass of Analytic Functions with Bounded Positive Real Part,"*Advances in Pure Mathematics*, Vol. 3 No. 4, 2013, pp. 409-414. doi: 10.4236/apm.2013.34059.

Y. Sim and O. Kwon, "A Certain Subclass of Analytic Functions with Bounded Positive Real Part,"

References

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[2] H. M. Srivastava, A. K. Mishra and P. Gochhayat, “Certain Subclasses of Analytic and Bi-Univalent Functions,” Applied Mathematics Letters, Vol. 23, No. 10, 2010, pp. 1188-1192. doi:10.1016/j.aml.2010.05.009

[3] Q.-H. Xu, Y.-C. Gui and H. M. Srivastava, “Coefficient Estimates for a Certain Subclass of Analytic and Bi-Univalent Functions,” Applied Mathematics Letters, Vol. 25, No. 6, 2012, pp. 990-994. doi:10.1016/j.aml.2011.11.013

[4] R. M. Ali, K. Lee, V. Ravichandran and S. Supramaniam, “Coefficient Estimates for Bi-Univalent Ma-Minda Starlike and Convex Functions,” Applied Mathematics Letters, Vol. 25, No. 3, 2012, pp. 344-351.

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[6] W. Rogosinski, “On the Coefficients of Subordinate Functions,” Proceeding of the London Mathematical Society, Vol. 2, No. 48, 1943, pp. 48-62.

[7] F. Keogh and E. Merkers, “A Coefficient Inequality for Certain Classes of Analytic Functions,” Proceedings of the American Mathematical Society, Vol. 20, No. 1, 1969, pp. 8-12. doi:10.1090/S0002-9939-1969-0232926-9

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[1] K. Kuroki and S. Owa, “Notes on New Class for Certain Analytic Functions,” RIMS Kokyuroku 1772, 2011, pp. 21-25.

[2] H. M. Srivastava, A. K. Mishra and P. Gochhayat, “Certain Subclasses of Analytic and Bi-Univalent Functions,” Applied Mathematics Letters, Vol. 23, No. 10, 2010, pp. 1188-1192. doi:10.1016/j.aml.2010.05.009

[3] Q.-H. Xu, Y.-C. Gui and H. M. Srivastava, “Coefficient Estimates for a Certain Subclass of Analytic and Bi-Univalent Functions,” Applied Mathematics Letters, Vol. 25, No. 6, 2012, pp. 990-994. doi:10.1016/j.aml.2011.11.013

[4] R. M. Ali, K. Lee, V. Ravichandran and S. Supramaniam, “Coefficient Estimates for Bi-Univalent Ma-Minda Starlike and Convex Functions,” Applied Mathematics Letters, Vol. 25, No. 3, 2012, pp. 344-351.

[5] S. S. Miller and P. T. Mocanu, “Differential Subordinations, Theory and Applications,” Marcel Dekker, 2000.

[6] W. Rogosinski, “On the Coefficients of Subordinate Functions,” Proceeding of the London Mathematical Society, Vol. 2, No. 48, 1943, pp. 48-62.

[7] F. Keogh and E. Merkers, “A Coefficient Inequality for Certain Classes of Analytic Functions,” Proceedings of the American Mathematical Society, Vol. 20, No. 1, 1969, pp. 8-12. doi:10.1090/S0002-9939-1969-0232926-9

[8] P. Duren, “Univalent Functions,” Springer-Verlag, New York, 1983.