A Survey on Operator Monotonicity, Operator Convexity, and Operator Means
International Journal of Analysis, Volume 2015, Issue 1, 2015., 2015 This paper is an expository devoted to an important class of real‐valued functions introduced by Löwner, namely, operator monotone functions. This concept is closely related to operator convex/concave functions. Various characterizations for such functions are given from the viewpoint of differential analysis in terms of matrix of divided differences ...
Pattrawut Chansangiam, Julien Salomon
wiley +1 more source
Hermite‐Hadamard and Simpson‐Like Type Inequalities for Differentiable Harmonically Convex Functions
Journal of Mathematics, Volume 2014, Issue 1, 2014., 2014 A new identity for differentiable functions is derived. A consequence of the identity is that the author establishes some new general inequalities containing all of the Hermite‐Hadamard and Simpson‐like types for functions whose derivatives in absolute value at certain power are harmonically convex.
İmdat İşcan, Roberto A. Kraenkel
wiley +1 more source
New General Integral Inequalities for Lipschitzian Functions via Hadamard Fractional Integrals
International Journal of Analysis, Volume 2014, Issue 1, 2014., 2014 The author obtains new estimates on generalization of Hadamard, Ostrowski, and Simpson type inequalities for Lipschitzian functions via Hadamard fractional integrals. Some applications to special means of positive real numbers are also given.
İmdat İşcan, Julien Salomon
wiley +1 more source
A New Class of Operator Monotone Functions via Operator Means
, 2016 In this paper, we obtain a new class of functions, which is developed via the Hermite--Hadamard inequality for convex functions. The well-known one-one correspondence between the class of operator monotone functions and operator connections declares that
Aujla, J. S. +3 more
core +1 more source
Sharp Inequalities for Trigonometric Functions
Abstract and Applied Analysis, Volume 2014, Issue 1, 2014., 2014 We establish several sharp inequalities for trigonometric functions and present their corresponding inequalities for bivariate means.
Zhen-Hang Yang +4 more
wiley +1 more source
On Trapezoid Inequality Via a Grüss Type Result and Applications [PDF]
, 1999 In this paper, we point out a Grüss type inequality and apply it for special means (logarithmic mean, identric mean, etc...
Dragomir, Sever S, McAndrew, Alasdair
core
New sharp bounds for identric mean in terms of logarithmic mean and arithmetic mean [PDF]
Journal of Mathematical Inequalities, 2012 Let x,y>0 with xy. We give new sharp bounds for identric mean I =e −1 (x x /y y ) 1/(x−y) in terms of logarithmic mean L =( x −y)/(lnx −lny) and arithmetic mean A =( x+y)/2: 1 2 L p0 + 1 2 A p0 1/p0 < I < 1 2 L ˜ p0 + 1 2 A ˜ p0 1/ ˜ p0 ,
openaire +1 more source
Some sharp inequalities involving Seiffert and other means and their concise proofs [PDF]
, 2012 In the paper, by establishing the monotonicity of some functions involving the sine and cosine functions, the authors provide concise proofs of some known inequalities and find some new sharp inequalities involving the Seiffert, contra-harmonic ...
Jiang, Wei-Dong, Qi, Feng
core +1 more source
A Class of Logarithmically Completely Monotonic Functions and Their Applications
Journal of Applied Mathematics, Volume 2014, Issue 1, 2014., 2014 We study the recent investigations on a class of functions which are logarithmically completely monotonic. Two open problems are also presented.
Senlin Guo, Qiu-Ming Luo
wiley +1 more source
Hall Normalization Constants for the Bures Volumes of the n-State Quantum Systems
, 1999 We report the results of certain integrations of quantum-theoretic interest, relying, in this regard, upon recently developed parameterizations of Boya et al of the n x n density matrices, in terms of squared components of the unit (n-1)-sphere and the n
Bateman P T +46 more
core +1 more source