Some New Generalizations of Zygmund–type Inequalities for Polynomials
نویسندگان
چکیده
In this paper, we consider a problem of investigating the dependence of ∥∥∥P(Rz)−αP(rz)+β {( R+1 r +1 )n −|α | ∥∥∥ p on ‖P(z)‖p for arbitrary real or complex numbers α , β with |α | 1 , |β | 1 , R > r 1 , p > 0 and present certain sharp compact generalizations of some well-known Zygmund-type inequalities for polynomials, from which a variety of interesting results follows as special cases. Mathematics subject classification (2010): 30D15, 41A17.
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