A unified study of certain subclasses of alpha-uniformly convex functions of order beta with negative coefficients

Abstract

In this paper, we introduce a unified presentation of certain subclasses of starlike and uniformly convex functions with negative coefficients. The unified class of starlike and uniformly convex functions with negative coefficients in the open unit disc is denoted by α-T(β, μ). It is interesting to note that the results of this paper are sharp and generalize the corresponding results of Bharti et al. [1], Dixit and Misra [2] and hence corresponding results of Murugusundaramoorthy [9], Goodman [3,4], Ma and Minda [7,8], Ronning [10], Kanas and Wisniowska [5,6].