Techniques of the Differential Subordination for Domains Bounded by Conic Sections
نویسنده
چکیده
We solve the problem of finding the largest domain D for which, under given ψ and q, the differential subordination ψ(p(z),zp′(z)) ∈ D ⇒ p(z) ≺ q(z), where D and q( ) are regions bounded by conic sections, is satisfied. The shape of the domain D is described by the shape of q( ). Also, we find the best dominant of the differential subordination p(z)+ (zp′(z)/(βp(z)+γ)) ≺ pk(z), when the function pk (k∈ [0,∞)) maps the unit disk onto a conical domain contained in a right half-plane. Various applications in the theory of univalent functions are also given.
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