Abstract
We will show certain functional inequalities involving fractional powers, making use of the Furuta inequality and Tanahashi’s argument. MSC:26D07, 26A09, 39B62, 47A63.
Highlights
Let x be an arbitrary positive real number
At least to the author, it seems not easy to give an elementary proof of the inequality which has a very similar form to the preceding one their corresponding numerical parts are different
Let us recall some fundamental concepts on related matrix inequalities
Summary
Let x be an arbitrary positive real number. One can see the inequality x – ≤x (x – ), for instance, is reduced to a simple polynomial inequality by putting t =at least to the author, it seems not easy to give an elementary proof of the inequality √√ – + √ √√ + x – ≤ √ √√. Abstract We will show certain functional inequalities involving fractional powers, making use of the Furuta inequality and Tanahashi’s argument. 1 Introduction Let x be an arbitrary positive real number. At least to the author, it seems not easy to give an elementary proof of the inequality which has a very similar form to the preceding one their corresponding numerical parts are different.
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