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For a certain linear operator which is defined by means of the Hadamard product (or convolution) with a generalized hypergeometric function, the authors aim at investigating various mapping and inclusion properties involving such subclasses of analytic and univalent functions as (for example) k-uniformly convex functions and k-starlike functions. Relevant connections of the definitions and results...
Let the function pa,b,s-so with a, b real, nonnegative numbers and s, so is an element of R, be a conform al mapping of the unit disk onto a hyperbolic domain. We establish the conditions udner which the differential subordination of the type p(z) +[...]zp'(z) -< pa,b,s-so(^) yields p -< pa,b,s- so(z) yields p [...] pa,b,s in U. Some applications of obtained results are given.
Let k-UCV denote the class of k-uniformly convex functions and let k-ST be the related class of k-starlike functions. For [..] > 0 and nonnegative sequence {tn] we define generalized neighbourhood [...].
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