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 functio...

This paper is related to notions adapted from fuzzy set theory the field of complex analysis, namely differential subordinations. work aims present new subordinations for which best dominant and subordinate are given, respectively. The original theorems proved in generate interesting corollaries particular choices functions acting as dominant. Here, this article, subordination results obtained ...

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