On refined Young inequalities and reverse inequalities

By Shigeru Furuichi. 2010

94 citations recorded by the source corpus.

In this paper, we show refined Young inequalities for two positive operators. Our results refine the ordering relations among the arithmetic mean, the geometric mean and the harmonic mean for two positive operators. In addition, we give two different reverse inequalities for the refined Young inequality for two positive operators.

Subfields: Applied Mathematics, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/5b89dd69d3a01349b0623bf81c6d6c1570cae9cf

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Applied Mathematics

1. Junliang Wu
2. Jianguo Zhao
3. Wenshi Liao
4. Nicucsor Minculete
5. I. N. Cangul
6. Nihat Akgunes
7. A. Yurttaş
8. M. Togan

In Mathematical Physics

1. Junliang Wu
2. Jianguo Zhao
3. Wenshi Liao
4. I. N. Cangul
5. Nihat Akgunes
6. A. Yurttaş
7. M. Togan
8. A. Cevik

Citations in the corpus

• NEW VERSIONS OF REVERSE YOUNG AND HEINZ MEAN INEQUALITIES WITH THE KANTOROVICH CONSTANT (2015, methodology): “Furuichi with a different technique, but our method is more transparent and simpler than the one given in [10].”
• Alternative reverse inequalities for Young's inequality (2011, background): “[7] S.”
• REFINED YOUNG INEQUALITY WITH KANTOROVICH CONSTANT (2011, background): “See [3, 4] for recent developments of the improved Young inequality.”
• On the first Zagreb index and multiplicative Zagreb coindices of graphs (2016, methodology): “The following inequality was obtained by Furuichi [12].”