<abstract xmlns="http://www.w3.org/1999/xhtml">

<p>In this article, we mainly study the interpolations between arithmetic mean and geometric mean—power mean, Heron mean and Heinz mean. First, we obtain the improvement and reverse improvement of arithmetic-power mean inequalities by the convexity of the function. We show that the proof of Heron mean inequality due to Yang and Ren: [<italic>Some results of Heron mean and Young’s inequalities</italic>, J. Inequal. Appl. <bold>2018</bold> (2018), paper no, 172], is not substantial. In addition, we also obtain Heron-Heinz mean inequalities for <italic>t</italic> ∈ ℝ. Further corresponding operator versions and generalizations are also established.</p>
</abstract>

In this article, we mainly study the interpolations between arithmetic mean and geometric mean—power mean, Heron mean and Heinz mean. First, we obtain the improvement and reverse improvement of arithmetic-power mean inequalities by the convexity of the function. We show that the proof of Heron mean inequality due to Yang and Ren: [Some results of Heron mean and Young’s inequalities, J. Inequal. Appl. 2018 (2018), paper no, 172], is not substantial. In addition, we also obtain Heron-Heinz mean inequalities for t ∈ ℝ. Further corresponding operator versions and generalizations are also established.

Some Inequalities Involving Interpolations Between Arithmetic and Geometric Mean

Tatra Mountains Mathematical Publications

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.

{"article-title":"Some Inequalities Involving Interpolations Between Arithmetic and Geometric Mean"}

In this article, we mainly study the interpolations between arithmetic mean and geometric mean—power mean, Heron mean and Heinz mean. First, we obtain the...

Some Inequalities Involving Interpolations Between Arithmetic and Geometric Mean

Published Online: Nov 29, 2022

Page range: 93 - 106

Received: May 27, 2022

DOI: https://doi.org/10.2478/tmmp-2022-0007

Keywords
the weighted power mean, Heron mean, Heinz mean, operator inequalities

© 2022 Hongliang Zuo et al., published by Sciendo

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.

Some Inequalities Involving Interpolations Between Arithmetic and Geometric Mean

Published Online: Nov 29, 2022

Page range: 93 - 106

Received: May 27, 2022

DOI: https://doi.org/10.2478/tmmp-2022-0007

Keywordsthe weighted power mean, Heron mean, Heinz mean, operator inequalities

© 2022 Hongliang Zuo et al., published by Sciendo

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.

Keywords
the weighted power mean, Heron mean, Heinz mean, operator inequalities