Generalizations of Bernstein and Turán-Type Inequalities for the Polar Derivative of a Complex Polynomial
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DOI: 10.1007/s00009-019-1446-3
Abstract: The goal of this paper is to extend to the polar derivatives some previous inequalities between the $$L^\gamma $$-norms of the derivative and of the polynomial itself, in case when the zeros are outside or… read more here.
Keywords: polar derivative; generalizations bernstein; tur type; bernstein tur ... See more keywords
The Turán-Type Inequality in the Space L0 on the Unit Interval
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DOI: 10.1007/s10476-021-0097-3
Abstract: Let P(x) be an arbitrary algebraic polynomial of degree n with all zeros in the unit interval −1 ≤ x ≤ 1. We establish the Turan-type inequality ‖P″‖0 ≥ n(e/4)‖P‖0, where $${\left\| f \right\|_0} =… read more here.
Keywords: tur type; inequality; type inequality; unit interval ... See more keywords
Logconcavity, twice-logconcavity and Turán-type inequalities
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DOI: 10.1007/s10479-018-2923-y
Abstract: This paper presents a brief review of the logconcavity of some compound distributions and its relationship to Turán-type inequalities. Further, we introduce a new concept of twice-logconcavity (twice-logconvexity) and show that many discrete probability distributions… read more here.
Keywords: logconcavity; tur type; logconcavity twice; type inequalities ... See more keywords