Abstract

In the present paper, the author introduce two new subclasses ${\Cal S}_{sc}^{(k)}(\alpha,\beta,\gamma)$ of close-to-convex functions and ${\Cal C}_{sc}^{(k)}(\alpha,\beta,\gamma)$ of quasi-convex functions with respect to $2k$-symmetric conjugate points. The coefficient inequalities and integral representations for functions belonging to these classes are provided, the inclusion relationships and convolution conditions for these classes are also provided.

Keywords: Close-to-convex functions, quasi-convex functions, differential subordination, Hadamard product, $2k$-symmetric conjugate points.

MSC: 30C45

Pages:  65$-$73     

Volume  59 ,  Issue  1$-$2 ,  2007