A complete refinement of Young's inequality

“…Matrix inequalities that correspond to Theorems 4 and 5 have been already established in papers [2,12]. Now, we are going to discuss matrix inequalities that correspond to Corollary 8, closely connected to some recent matrix inequalities due to Dragomir. In order to do this, we will first generalize the definition of the geometric mean A♯ v B = A 1/2 (A −1/2 BA −1/2 ) v A 1/2 .…”

Section: Applications To Some Matrix Inequalitiesmentioning

confidence: 85%

Improved Jensen-type inequalities via linear interpolation and applications

Choi¹,

Krnić²,

Pečarić³

2017

Journal of Mathematical Inequalities

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Abstract. In this paper we develop a general method for improving Jensen-type inequalities for convex and, even more generally, for piecewise convex functions. Our main result relies on the linear interpolation of a convex function. As a consequence, we obtain improvements of some recently established Young-type inequalities. Finally, our method is also applied to matrix case. In such a way we obtain improvements of some important matrix inequalities known from the literature.Mathematics subject classification (2010): 26D15, 26A51, 15A45.

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“…Thus, when N = 1, (3.2) provides a "negative" version of this refinement. In our recent work [8], Young's inequality has been refined by adding as many terms as we wish. Earlier, the squared version…”

Section: 1mentioning

confidence: 99%

Convex functions and means of matrices

Sababheh¹

2017

Mathematical Inequalities &Amp; Applications

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Abstract. In this article, we prove that convex functions and log-convex functions obey certain general refinements that lead to several refinements and reverses of well known inequalities for matrices, including Young's inequality, Heinz inequality, the arithmetic-harmonic and the geometric-harmonic mean inequalities.Mathematics subject classification (2010): 15A39, 15A60, 15B48, 26A51, 47A30, 47A60, 47A63.

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A complete refinement of Young's inequality

Cited by 42 publications

References 12 publications

Convexity and matrix means

Convexity and matrix means

Improved Jensen-type inequalities via linear interpolation and applications

Convex functions and means of matrices

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