Some criteria for higher order Turán inequalities in the spirit of Mařík's theorem

Abstract

By using Mařík's theorem and the theory of multiplier sequences, we give some sufficient conditions for proving the higher order Turán inequalities for nonnegative sequences. As an immediate consequence, we present a simple proof of the higher order Turán inequalities for the Boros–Moll sequence, which were recently established by Jeremy Guo and then reproved by James Zhao.

Keywords:

• Mařík's theorem
• real zeros
• higher order Turán inequality
• multiplier sequence

AMS Mathematics Subject Classification 2010:

• 05A20
• 30C15

Disclosure statement

No potential conflict of interest was reported by the author(s).

Additional information

Funding

Supported by the Fundamental Research Funds for the Central Universities and the National Natural Science Foundation of China [grant number 11971249].