A Certain Subclass of Analytic Functions

¹ Department of Mathematics, Kyungsung University, Busan, Korea (South)

² Department of Mathematics, Kyungsung University, Busan, Korea (South)

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.

KeywordsUnivalent FunctionsConvex FunctionsSubordinationOrder of Convexity

J. Sokó?, “A Certain Class of Starlike Functions,” Computers and Mathematics with Applications , Vol. 62, No. 2, 2011, pp. 611-619. doi:10.1016/j.camwa.2011.05.041
M. S. Rovertson, “Certain Classes of Starlike Functions,” Michigan Mathematical Journal , Vol. 76, No. 1, 1954, pp. 755-758.
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.
W. Janowski, “Some Extremal Problems for Certain Families of Analytic Functions,” Annales Polonici Mathematici , Vol. 28, 1973, pp. 297-326.
R. Jurasiska and J. Stankiewics, “Coefficients in Some Classes Defined by Subordination to Multivalent Majorants,” Annales Polonici Mathematici , Vol. 80, 2003, pp. 163-170.
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.
P. Duren, “Univalent functions, A Series of Comprehensive Studies in Mathematics,” Vol. 259, Springer-Verlag, New-York, 1983.

Menu

A Certain Subclass of Analytic Functions

Abstract

References (7)