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.
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I would like to thank referees for their careful reading of the manuscript and for their remarks and suggestions.
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Nishizawa, Y. The Best Possible Constants of the Inequalities with Power Exponential Functions. Indian J Pure Appl Math 51, 1761–1768 (2020). https://doi.org/10.1007/s13226-020-0495-4
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DOI: https://doi.org/10.1007/s13226-020-0495-4
Key words
- Inequalities
- power exponential functions
- monotonically increasing functions
- monotonically decreasing functions