On the Schur inequality

1979 ◽  
Vol 7 (4) ◽  
pp. 343-357 ◽  
Author(s):  
J. A. Dias Da Silva
Keyword(s):  
Schur Inequality

scholarly journals Some Properties and Inequalities for the h,s-Nonconvex Functions

2020 ◽  
Vol 2020 ◽  
pp. 1-8
Author(s):  
Chengli Wang ◽  
Muhammad Shoaib Saleem ◽  
Hamood Ur Rehman ◽  
Muhammad Imran
Keyword(s):  
Jensen Inequality ◽  
Weighted Version ◽  
Hadamard Inequality ◽  
Basic Properties ◽  
Nonconvex Functions ◽  
Schur Inequality ◽  
Class Of Functions

The purpose of this paper is to introduce the notion of strongly h,s-nonconvex functions and to present some basic properties of this class of functions. We present Schur inequality, Jensen inequality, Hermite–Hadamard inequality, and weighted version of the Hermite–Hadamard inequality.

scholarly journals The Integral Form of the Schur Inequality

2020 ◽  
Vol 17 (2) ◽  
pp. 36-40
Author(s):  
Béla Finta
Keyword(s):  
Integral Form ◽  
Schur Inequality

AbstractThe purpose of this paper is to show the integral form of the original Schur inequality and to give some applications.

scholarly journals Some Refinements and Generalizations of I. Schur Type Inequalities

2014 ◽  
Vol 2014 ◽  
pp. 1-8
Author(s):  
Xian-Ming Gu ◽  
Ting-Zhu Huang ◽  
Wei-Ru Xu ◽  
Hou-Biao Li ◽  
Liang Li ◽  
...  
Keyword(s):  
Lower Bounds ◽  
Recent Literature ◽  
Structural Characteristics ◽  
Variable Parameter ◽  
Upper Bounds ◽  
Upper And Lower Bounds ◽  
Numerical Examples ◽  
Schur Inequality

Recently, extensive researches on estimating the value ofehave been studied. In this paper, the structural characteristics of I. Schur type inequalities are exploited to generalize the corresponding inequalities by variable parameter techniques. Some novel upper and lower bounds for the I. Schur inequality have also been obtained and the upper bounds may be obtained with the help ofMapleand automated proving package (Bottema). Numerical examples are employed to demonstrate the reliability of the approximation of these new upper and lower bounds, which improve some known results in the recent literature.

scholarly journals An extension of the generalised schur inequality

1995 ◽  
Vol 52 (2) ◽  
pp. 341-343
Author(s):  
B. Mond ◽  
J.E. Pečarić
Keyword(s):  
Schur Inequality ◽  
The Absolute

The well-known Schur inequality relates the sum of the squares of the absolute values of the eigenvalues of A to the elements of A. This was recently generalised to powers between one and two. Here we show that the inequality holds for powers between zero and two.

scholarly journals On inequalities for integral operators

1970 ◽  
Vol 11 (2) ◽  
pp. 126-133 ◽  
Author(s):  
G. O. Okikiolu
Keyword(s):  
General Setting ◽  
Integral Operators ◽  
The Other ◽  
Special Cases ◽  
Measure Spaces ◽  
Schur Inequality ◽  
Abstract Measure ◽  
Schur Theorem ◽  
Image Position ◽  
Similar Extension

In two papers [3] and [4], the author has extended the inequality of Schur (Theorem 319 of [2]) to cases involving kernels which satisfy identities of the formThe purpose of this paper is to prove a general inequality, which includes the above and also the inequality of Young (Theorem 281 of [2]) as special cases. We shall give the results a general setting by considering functions defined on abstract measure spaces. From this we shall deduce an extension to n dimensions of the results given in [3], which also generalises a similar extension of the Schur inequality given by Stein and Weiss. In fact some cases of the other results given in [5] will follow directly from our theorem.

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