A Certain Subclass of Analytic Functions

ABSTRACT

In the present paper, we introduce a class of analytic functions in the open unit disc by using the analytic function q_{α}(z)=3/(3+(*α*-3)z-*α*z^{2}), which was investigated by Sokó? [1]. We find some properties including the growth theorem or the coefficient problem of this class and we find some relation with this new class and the class of convex functions.

In the present paper, we introduce a class of analytic functions in the open unit disc by using the analytic function q

Cite this paper

Y. Sim and O. Kwon, "A Certain Subclass of Analytic Functions,"*Advances in Pure Mathematics*, Vol. 2 No. 4, 2012, pp. 291-295. doi: 10.4236/apm.2012.24038.

Y. Sim and O. Kwon, "A Certain Subclass of Analytic Functions,"

References

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[2] M. S. Rovertson, “Certain Classes of Starlike Functions,”*Michigan Mathematical Journal*, Vol. 76, No. 1, 1954, pp. 755-758.

[3] W. Janowski, “Extremal Problems for a Family of Functions with Positive Real Part and Some Related Families,”*Annales Polonici Mathematici*, Vol. 23, 1970, pp. 159-177.

[4] W. Janowski, “Some Extremal Problems for Certain Families of Analytic Functions,”*Annales Polonici Mathematici*, Vol. 28, 1973, pp. 297-326.

[5] R. Jurasiska and J. Stankiewics, “Coefficients in Some Classes Defined by Subordination to Multivalent Majorants,”*Annales Polonici Mathematici*, Vol. 80, 2003, pp. 163-170.

[6] S. S. Miller and P. T. Mocanu, “Differential Subordinations, Theory and Applications,”* Series of Monographs and Textbooks in Pure and Applied Mathematics*, Vol. 225, Marcel Dekker Inc., New York, 2000.

[7] P. Duren, “Univalent functions, A Series of Comprehensive Studies in Mathematics,” Vol. 259, Springer-Verlag, New-York, 1983.

[1] J. Sokó?, “A Certain Class of Starlike Functions,”

[2] M. S. Rovertson, “Certain Classes of Starlike Functions,”

[3] W. Janowski, “Extremal Problems for a Family of Functions with Positive Real Part and Some Related Families,”

[4] W. Janowski, “Some Extremal Problems for Certain Families of Analytic Functions,”

[5] R. Jurasiska and J. Stankiewics, “Coefficients in Some Classes Defined by Subordination to Multivalent Majorants,”

[6] S. S. Miller and P. T. Mocanu, “Differential Subordinations, Theory and Applications,”

[7] P. Duren, “Univalent functions, A Series of Comprehensive Studies in Mathematics,” Vol. 259, Springer-Verlag, New-York, 1983.