Results 11 to 20 of about 18,915 (259)

Refined Young Inequality and Its Application to Divergences

Entropy, 2021
We give bounds on the difference between the weighted arithmetic mean and the weighted geometric mean. These imply refined Young inequalities and the reverses of the Young inequality. We also studied some properties on the difference between the weighted
Shigeru Furuichi, Nicuşor Minculete
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On approximating the quasi-arithmetic mean

Journal of Inequalities and Applications, 2019
In this article, we prove that the double inequalities α1[7C(a,b)16+9H(a,b)16]+(1−α1)[3A(a,b)4+G(a,b)4]
Tie-Hong Zhao, Bu-Chuan Zhou, Miao-Kun Wang, Yu-Ming Chu   +3 more
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Additive Refinements and Reverses of Young's Operator Inequality Via a Result of Cartwright and Field

Universal Journal of Mathematics and Applications, 2021
In this paper we obtain some new additive refinements and reverses of Young's operator inequality via a result of Cartwright and Field. Comparison with other additive Young's type inequalities are also provided.
Sever Dragomır
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Optimal bounds for arithmetic-geometric and Toader means in terms of generalized logarithmic mean

Journal of Inequalities and Applications, 2017
In this paper, we find the greatest values α 1 , α 2 $\alpha_{1},\alpha_{2}$ and the smallest values β 1 , β 2 $\beta_{1},\beta_{2}$ such that the double inequalities L α 1 ( a , b ) < AG ( a , b ) < L β 1 ( a , b ) $L_{\alpha_{1}}(a,b)0$ with a ≠ b $a ...
Qing Ding, Tiehong Zhao
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Arithmetic–Geometric Mean determinantal identity

Linear Algebra and its Applications, 2011
For any \(n\) by \(n\) matrix \(A\), let \(A_{r}\left[ i,j\right] \) denote an \(r\) by \(r\) submatrix consisting of r contiguous rows and columns of \(A\), starting with row \(i\) and column \(j\). Let also the superscript \(t\) stands for transposition of a matrix and \(J_{n}\) be an all-one matrix of order \(n\).
Bayat, M., Teimoori, H.
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Further Improved Weighted Arithmetic-Geometric Operator Mean Inequalities

Mathematics, 2019
The main purpose of this paper is to present some weighted arithmetic-geometric operator mean inequalities. These inequalities are refinements and generalizations of the corresponding results.
Jianming Xue, Xingkai Hu
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Some picture fuzzy mean operators and their applications in decision-making [PDF]

Journal of Fuzzy Extension and Applications, 2022
Picture fuzzy set is the generalization of fuzzy set and intuitionistic fuzzy set. It is useful for handling uncertainty by considering the positive membership, neutral membership and negative membership degrees independently for each element of a ...
Hasan Mohammad Kamrul, Ali Md. Yasin, Sultana Abeda, Mitra Nirmal Kanti   +3 more
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Sharp two-parameter bounds for the identric mean

Journal of Inequalities and Applications, 2018
For t∈[0,1/2] $t\in [0,1/2]$ and s≥1 $s\ge 1$, we consider the two-parameter family of means Qt,s(a,b)=Gs(ta+(1−t)b,(1−t)a+tb)A1−s(a,b), $$ Q_{t,s}(a,b)=G^{s}\bigl(ta+(1-t)b,(1-t)a+tb\bigr)A^{1-s}(a,b), $$ where A and G denote the arithmetic and ...
Omran Kouba
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A Generalization of the Inequality of the Arithmetic-Geometric Means [PDF]

Proceedings of the Glasgow Mathematical Association, 1956
The main result in this paper, contained in Theorem 1, is a generalisation of the inequality of the arithmetic-geometric means. A result of a similar character has been proved by Siegel (2). The present result gives an improvement in the inequality in the case when the variables involved are not all distinct, whereas Siegel's result does not.
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Computation of π Using Arithmetic-Geometric Mean [PDF]

Mathematics of Computation, 1976
A new formula for π \pi is derived. It
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