Majorization problems and integral transforms for a Class of Univalent Functions with missing coefficients
Abstract
In 2005, Ponnusamy and Sahoo have introduced a special subclass of univalent functions Un(\lambda) (n 2 N, > 0) and obtained some geometrical properties, including strongly starlikeness and convexity, for the functions of this subclass Un(). Moreover, they have studied some important properties of an integral transform connected with these subclasses. The aim of the present paper is to investigate another important concept of majorization for the functions belonging to the class Un(\lambda) (0 <\lambda=< 1). We shall also discuss a majorization problem for some special integral transforms.
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References
O. Altinas, Majorization for certain analytic functions, Eur. J. Pure Appl. Math., 5(1)(2012), 16-23.
O. Altinas, Ö. Özkan and H. M. Srivastava, Majorization by starlike functions of complex order, Complex Var., 46(2001), 207-218.
P. L. Duren, Univalent functions, Springer-Verlag, New York, Berlin, Heidelberg, Tokyo, 1983.
A. W. Goodman, Univalent functions, Vol. I and Vol. II, Mariner Publishing Company, Tampa, Florida, 1983.
S. P. Goyal and P. Goswami, Majorization for certain classes of analytic functions defined by fractional derivatives, Appl. Math. Lett., 22(12)(2009), 1855-1858.
S. P. Goyal and P. Goswami, Majorization for certain classes of meromorphic functions defined by integral operator, Annales. Univ. Mariae Curie-Skłodowska, LXVI(2)(2012), 57-62.
J. K. Prajapat and M. K. Aouf, Majorization problem for certain class of p-valently analytic function defined by generalized fractional differintegral operator, Comput. Math. Appl., 63(1)(2012), 42-47.
K. Kuroki, T. Hayami, N. Uyanik and S. Owa, Some properties for a certain class concerned with univalent functions, Comput. Math. Appl., 63(2012), 1425-1432.
S. H. Li, H. Tang and E. Ao, Majorization properties for certain new classes of analytic functions using the Salagean operator, J. Ineq. Appl. 2013, 2013:86.
T. H. MacGregor, Majorization by univalent functions, Duke Math. J., 34(1967), 95-102.
Z. Nehari, Conformal Mappings, Mc Graw-Hill, New York (1952).
M. Obradović, A class of univalent functions, Hokkaido Math. J., 27(1998), 329-335.
M. Obradović and S. Ponnusamy, New criteria and distortion theorems for univalent functions, Complex Variables: Theory and Appl., 44(2001), 173-191.
M. Obradović and S. Ponnusamy, Univalence and starlikeness of certain integral transforms defined by convolution of analytic functions, J. Math. Anal. Appl., 336(2007), 758-767.
S. Ponnusamy, Starlikeness criteria for a certain class of analytic functions, Appl. Math. Lett., 24(2011), 381-386.
S. Ponnusamy and P. Sahoo, Special classes of univalent functions with missing coefficients and integral transforms, Bull. Malays. Math. Sci. Soc., 28(2)(2005), 141-156.
M. S. Robertson, Quasi-subordination and coefficient conjectures, Bull. Amer. Math. Soc., 76(1970), 1-9.
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