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Let S s (α) (0 ≤ α < 1/2) be the class of functions f (z) = z +··· which are analytic in the unit disk and satisfy there Re{zf (z)/(f (z) − f (−z))} > α. In the present paper, we find the sharp lower bound on Re{(f (z) − f (−z))/z} and investigate two subclasses S 0 (α) and T 0 (α) of S s (α). We derive sharp distortion inequalities and some properties of… (More)

- DING-GONG YANG
- 2007

Making use of a linear operator, which is defined here by means of the Hadamard product (or convolution), we introduce a class Q p (a, c; h) of analytic and multivalent functions in the open unit disk. An inclusion relation and a convolution property for the class Q p (a, c; h) are presented. Some integral-preserving properties are also given.

- N-ENG XU, DING-GONG YANG
- 2013

Let A p (p ∈ N) be the class of functions f (z) = z p + ∞ m=1 a p+m z p+m which are analytic in the unit disk. By virtue of the Ruscheweyh derivatives we introduce the new sub-classes C p (n, α, β, λ, µ) of A p. Subordination relations, inclusion relations, convolution properties and a sharp coefficient estimate are obtained. We also give a sufficient… (More)