A unified class of analytic functions with negative coefficients
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Making use of the convolution product, we introduce a unified class of analytic functions with negative coefficients. Also, we obtain the coefficient bounds, extreme points, and radius of starlikeness for functions belonging to the generalized class P g T (λ, α, β). Furthermore, partial sums f k (z) of functions f(z) in the class P g (λ, α, β) are considered and sharp lower bounds for the ratios of the real parts of f(z) to f k (z) and f′(z) to f′ k (z) are determined. Relevant connections of the results with various known results are also considered.
Key words and phrasesAnalytic univalent starlikeness convexity Hadamard product (convolution) Convolution product uniformly convex uniformly starlike functions
2000 Mathematics Subject Classification30C45
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