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 APM  Vol.2 No.4 , July 2012
A Certain Subclass of Analytic Functions
Young Jae Sim, Oh Sang Kwon*
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Abstract: In the present paper, we introduce a class of analytic functions in the open unit disc by using the analytic function qα(z)=3/(3+(α-3)z-αz2), 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.
Keywords: Univalent Functions; Convex Functions; Subordination; Order of Convexity
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.
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.

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[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.

 
 
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