scholarly journals Further generalization, refinements of the Young inequality

2021 ◽  
Author(s):  
Mohamed Amine Ighachane ◽  
Mohamed Akkouchi
Keyword(s):  
Positive Definite ◽  
Young Inequality ◽  
Young’S Inequality ◽  
Positive Definite Matrices ◽  
Young's Inequality

In this paper, we show a new generalized refinement of Young's inequality. As applications we give some new generalized refinements of Young type inequalities for the traces, determinants, and norms of positive definite matrices.

scholarly journals A new generalized refinements of Young’s inequality

2021 ◽  
Vol 40 (5) ◽  
pp. 1197-1209
Author(s):  
Mohamed Amine Ighachane ◽  
Mohamed Akkouchi
Keyword(s):  
Positive Definite ◽  
Young’S Inequality ◽  
Positive Definite Matrices ◽  
Young's Inequality

In this paper, we show a new generalized refinement of Young's inequality. As applications we give some new generalized refinements of Young type inequalities for the traces, determinants, and norms of positive definite matrices.

scholarly journals A new generalization of two refined Young inequalities and applications

2020 ◽  
Vol 6 (2) ◽  
pp. 155-167
Author(s):  
M. A. Ighachane ◽  
M. Akkouchi
Keyword(s):  
Positive Definite ◽  
Young Inequality ◽  
Numerical Radius ◽  
Positive Definite Matrices

AbstractIn this paper, we prove that if a, b > 0 and 0 ≤ α ≤ 1, then for m = 1, 2, 3, . . . ,\matrix{ {r_0^m{{\left( {{a^{{m \over 2}}} - {b^{{m \over 2}}}} \right)}^2}} & { \le r_0^m\left( {{{{b^{m + 1}} - {a^{m + 1}}} \over {b - a}} - \left( {m + 1} \right){{\left( {ab} \right)}^{{m \over 2}}}} \right)} \cr {} & { \le {{\left( {\alpha a + \left( {1 - \alpha } \right)b} \right)}^m} - {{\left( {{a^\alpha }{b^{1 - \alpha }}} \right)}^m},} \cr }where r0 = min{α, 1 – α }. This is a considerable new generalization of two refinements of the Young inequality due to Kittaneh and Manasrah, and Hirzallah and Kittaneh, which correspond to the cases m = 1 and m = 2, respectively. As applications we give some refined Young type inequalities for generalized euclidean operator radius and the numerical radius of some well-know f -connection of operators and refined some Young type inequalities for the traces, determinants, and norms of positive definite matrices.

scholarly journals Multi-variable weighted geometric means of positive definite matrices

2011 ◽  
Vol 435 (2) ◽  
pp. 307-322 ◽  
Author(s):  
Hosoo Lee ◽  
Yongdo Lim ◽  
Takeaki Yamazaki
Keyword(s):  
Positive Definite ◽  
Positive Definite Matrices ◽  
Geometric Means
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