scholarly journals Inequalities for certain Classes of Convex Functions

1959 ◽  
Vol 11 (4) ◽  
pp. 231-235 ◽  
Author(s):  
L. Mirsky
Keyword(s):  
Simple Proof ◽  
Convex Functions ◽  
Stochastic Matrices ◽  
Doubly Stochastic ◽  
Fan Theorem ◽  
Special Cases ◽  
Gauge Functions ◽  
Ky Fan ◽  
Ky Fan Theorem ◽  
Symmetric Gauge

Making use of properties of doubly-stochastic matrices, I recently gave a simple proof (4) of a theorem of Ky Fan (Theorem 2b below) on symmetric gauge functions. I now propose to show that the same idea can be employed to derive a whole series of results on convex functions ; in particular, certain well-known inequalities of Hardy-Littlewood-Pólya and of Pólya will emerge as specìal cases.

scholarly journals An improvement of Ky Fan theorem for matrix eigenvalues

2005 ◽  
Vol 49 (5-6) ◽  
pp. 789-803 ◽  
Author(s):  
Hou-Biao Li ◽  
Ting-Zhu Huang
Keyword(s):  
Fan Theorem ◽  
Matrix Eigenvalues ◽  
Ky Fan ◽  
Ky Fan Theorem

scholarly journals Ky Fan theorem applied to Randić energy

2014 ◽  
Vol 459 ◽  
pp. 23-42 ◽  
Author(s):  
Ivan Gutman ◽  
Enide A. Martins ◽  
María Robbiano ◽  
Bernardo San Martín
Keyword(s):  
Fan Theorem ◽  
Ky Fan ◽  
Ky Fan Theorem

scholarly journals Wielandt and Ky-Fan theorem for matrix pairs

2003 ◽  
Vol 369 ◽  
pp. 77-93 ◽  
Author(s):  
Ivica Nakić ◽  
Krešimir Veselić
Keyword(s):  
Fan Theorem ◽  
Ky Fan ◽  
Ky Fan Theorem

scholarly journals Some improvements on the Ky Fan theorem for tensors

2021 ◽  
Vol 40 (2) ◽  
Author(s):  
Mohsen Tourang ◽  
Mostafa Zangiabadi
Keyword(s):  
Multilinear Algebra ◽  
Numerical Examples ◽  
Eigenvalue Localization ◽  
Fan Theorem ◽  
Linear Multilinear Algebra ◽  
Numer Math ◽  
Ky Fan ◽  
Localization Sets ◽  
Ky Fan Theorem ◽  
Perron Vector

AbstractThe improvements of Ky Fan theorem are given for tensors. First, based on Brauer-type eigenvalue inclusion sets, we obtain some new Ky Fan-type theorems for tensors. Second, by characterizing the ratio of the smallest and largest values of a Perron vector, we improve the existing results. Third, some new eigenvalue localization sets for tensors are given and proved to be tighter than those presented by Li and Ng (Numer Math 130(2):315–335, 2015) and Wang et al. (Linear Multilinear Algebra 68(9):1817–1834, 2020). Finally, numerical examples are given to validate the efficiency of our new bounds.

scholarly journals Sherman, Hermite-Hadamard and Fejér like inequalities for convex sequences and nondecreasing convex functions

Filomat ◽  
2017 ◽  
Vol 31 (8) ◽  
pp. 2321-2335 ◽  
Author(s):  
Marek Niezgoda
Keyword(s):  
Convex Functions ◽  
Stochastic Matrices ◽  
Matrix Methods ◽  
Doubly Stochastic ◽  
Doubly Stochastic Matrices

In this paper, we prove Sherman like inequalities for convex sequences and nondecreasing convex functions. Thus we develop some results by S. Wu and L. Debnath [19]. In consequence, we derive discrete versions for convex sequences of Petrovic and Giaccardi?s inequalities. As applications, we establish some generalizatons of Fej?r inequality for convex sequences. We also study inequalities of Hermite-Hadamard type. Thus we extend some recent results of Latreuch and Bela?di [8]. In our considerations we use some matrix methods based on column stochastic and doubly stochastic matrices.

scholarly journals A new generalization of some quantum integral inequalities for quantum differentiable convex functions

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
Yi-Xia Li ◽  
Muhammad Aamir Ali ◽  
Hüseyin Budak ◽  
Mujahid Abbas ◽  
Yu-Ming Chu
Keyword(s):  
Integral Inequality ◽  
Convex Functions ◽  
Integral Identity ◽  
Integral Inequalities ◽  
Quantum Integral ◽  
Special Cases

AbstractIn this paper, we offer a new quantum integral identity, the result is then used to obtain some new estimates of Hermite–Hadamard inequalities for quantum integrals. The results presented in this paper are generalizations of the comparable results in the literature on Hermite–Hadamard inequalities. Several inequalities, such as the midpoint-like integral inequality, the Simpson-like integral inequality, the averaged midpoint–trapezoid-like integral inequality, and the trapezoid-like integral inequality, are obtained as special cases of our main results.

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