The Best Possible Constants of the Inequalities with Power Exponential Functions

Yusuke Nishizawa ()
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Yusuke Nishizawa: Saitama University

Indian Journal of Pure and Applied Mathematics, 2020, vol. 51, issue 4, 1761-1768

Abstract: Abstract The author in [7] conjectured the following inequality; If a and b are nonnegative real numbers with a + b = 1/2, then the inequality 1/2 ≤ a(2b)k+ b(2a)k ≤ 1 holds for 0 ≤ k ≤ 1. In this paper, we shall prove the conjecture affirmatively and give the upper and lower estimation of the power exponential functions ab + ba for the nonnegative real numbers a and b with a + b = 2. Moreover, we pose some inequalities with power exponential functions.

Keywords: Inequalities; power exponential functions; monotonically increasing functions; monotonically decreasing functions; 26D10 (search for similar items in EconPapers)
Date: 2020
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DOI: 10.1007/s13226-020-0495-4

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