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The Schur-convexity of the mean of a convex function
Applied Mathematics Letters, 2009 The authors establish the Schur-convexity at the upper and lower limits of the integral for the mean of a convex function. Furthermore, a new proof of the inequality \[ f\bigg(\frac{a+b}{2}\bigg)=H(0) \leq H(t) \leq H(1)= \frac1{b-a}\int^ b_ a f(x)\,dx \] obtained by \textit{S. S. Dragomir} [J. Math. Anal. Appl. 167, No. 1, 49--56 (1992; Zbl 0758.26014)
Huan-nan Shi
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The NLMS Is Steady-State Schur-Convex
IEEE Signal Processing Letters, 2021In this work, we study the impact of input-spread on the steady-state excess mean squared error (EMSE) of the normalized least mean squares (NLMS) algorithm. First, we use the concept of majorization to order the input-regressors according to their spread.
Anum Ali +2 more
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Convex sets of schur stable and stable matrices
Linear and Multilinear Algebra, 2000 Elsner L, Szulc T. Convex sets of Schur stable and stable matrices. Linear and Multilinear Algebra. 2000;48(1):1-19.We derive characterizations for the Schur stability and the stability of all convex combinations of k, k greater than or equal to2, given ...
Tomasz Szulc, Ludwig Elsner
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Strong Schur-Convexity of the Integral Mean
Results in Mathematics, 2023The strong Schur-convexity of the integral mean as well as of the left and right gaps in the Hermite- Hadamard inequality for strongly convex functions are proved. An useful characterization of strongly Schur convex functions F : I-n -> R by partial derivatives is given.
Mirosław Adamek +2 more
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Schur convexity for some differences of convex functions
Rocky Mountain Journal of Mathematics, 2021zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Safaei, Nozar, Barani, Ali
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Ukrainian Mathematical Journal, 2009
For x = (x 1, x 2, …, x n ) ∈ (0, 1 ] n and r ∈ { 1, 2, … , n}, a symmetric function F n (x, r) is defined by the relation $$ {F_n ...
Wei-Feng Xia, Yu-Ming Chu
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For x = (x 1, x 2, …, x n ) ∈ (0, 1 ] n and r ∈ { 1, 2, … , n}, a symmetric function F n (x, r) is defined by the relation $$ {F_n ...
Wei-Feng Xia, Yu-Ming Chu
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Convex combinations of matrices-nonsingularity and schur stability characterizations
Linear and Multilinear Algebra, 1998 Elsner L, Szulc T. Convex combinations of matrices - nonsingularity and schur stability characterizations. Linear and Multilinear Algebra.
Tomasz Szulc, Ludwig Elsner
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2010
For any given partial ordering \(\preceq\)of a setX, real-valued functionsf1 defined onXwhich satisfyf(x)= f(y) wheneverx_yare var- 2 iously referred to as “monotonic,” “isotonic,” or “order-preserving.” 3 For the ordering of majorization, the order-preserving functions were 4 first systematically studied by I. Schur (1923).
Albert W. Marshall +2 more
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For any given partial ordering \(\preceq\)of a setX, real-valued functionsf1 defined onXwhich satisfyf(x)= f(y) wheneverx_yare var- 2 iously referred to as “monotonic,” “isotonic,” or “order-preserving.” 3 For the ordering of majorization, the order-preserving functions were 4 first systematically studied by I. Schur (1923).
Albert W. Marshall +2 more
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Majorization and Schur Convexity with Respect to Partial Orders
Mathematics of Operations Research, 1993Majorization and Schur convexity constitute an important tool for establishing inequalities, in particular, due to the Schur-Ostrowski Theorem which provides a simple characterization of Schur convex functions through local two-coordinate conditions. However, the usefulness of the approach is limited by two stringent requirements.
Frank K. Hwang, Uriel G. Rothblum
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Schur-convexity and quadrature formulae
Mathematische Nachrichten, 2015This paper aims to contribute to the exploration of quadrature formulae by proving that the error of a quadrature formula has the Schur-convexity property. The emphasis is on the quadrature formulae with the maximum degree of precision. The Schur-convexity of the error has an interesting implication – the monotonicity of the error. Namely, it turns out
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