scholarly journals External Jensen-type operator inequalities via superquadraticity

2020 ◽  
pp. 31-31
Author(s):  
Mohsen Kian ◽  
Mario Krnic ◽  
Mohsen Delavar
Keyword(s):  
Type Operator ◽  
Jensen Inequality ◽  
Operator Inequalities ◽  
Superquadratic Functions ◽  
Adjoint Operators ◽  
External Form

In this paper we establish several Jensen-type operator inequalities for a class of superquadratic functions and self-adjoint operators. Our results are given in the so-called external form. As an application, we give improvements of the H?lder?McCarthy inequality and the classical discrete and integral Jensen inequality in the corresponding external forms. In addition, the established Jensen-type inequalities are compared with the previously known results and we show that our results provide more accurate estimates in some general settings.

scholarly journals Interpolating Jensen-type operator inequalities for log-convex and superquadratic functions

Filomat ◽  
2018 ◽  
Vol 32 (13) ◽  
pp. 4523-4535
Author(s):  
Mojtaba Bakherad ◽  
Mohsen Kian ◽  
Mario Krnic ◽  
Seyyed Ahmadi
Keyword(s):  
Convex Function ◽  
Convex Functions ◽  
Type Operator ◽  
Operator Inequality ◽  
Operator Inequalities ◽  
Superquadratic Functions

Motivated by some recently established Jensen-type operator inequalities related to a convex function, in the present paper we derive several more accurate Jensen-type operator inequalities for certain subclasses of convex functions. More precisely, we obtain interpolating series of Jensen-type inequalities utilizing log-convex and non-negative superquadratic functions. In particular, we obtain the corresponding refinements of the Jensen-Mercer operator inequality for such classes of functions.

scholarly journals Operator inequalities of Jensen type

2013 ◽  
Vol 1 ◽  
pp. 9-21
Author(s):  
M. S. Moslehian ◽  
J. Mićić ◽  
M. Kian
Keyword(s):  
Convex Function ◽  
Type Operator ◽  
Operator Inequalities ◽  
Continuous Convex Function ◽  
Adjoint Operators

Abstract We present some generalized Jensen type operator inequalities involving sequences of self-adjoint operators. Among other things, we prove that if f : [0;1) → ℝ is a continuous convex function with f(0) ≤ 0, thenfor all operators Ci such that (i=1 , ... , n) for some scalar M ≥ 0, where and

scholarly journals Inequalities of Hardy Type via Superquadratic Functions with General Kernels and Measures for Several Variables on Time Scales

2020 ◽  
Vol 2020 ◽  
pp. 1-15
Author(s):  
H. M. Rezk ◽  
H. A. Abd El-Hamid ◽  
A. M. Ahmed ◽  
Ghada AlNemer ◽  
M. Zakarya
Keyword(s):  
Time Scales ◽  
Time Scale ◽  
Minkowski Inequality ◽  
Jensen Inequality ◽  
Hardy Type ◽  
Several Variables ◽  
Special Cases ◽  
Superquadratic Functions

We use the properties of superquadratic functions to produce various improvements and popularizations on time scales of the Hardy form inequalities and their converses. Also, we include various examples and interpretations of the disparities in the literature that exist. In particular, our findings can be seen as refinements of some recent results closely linked to the time-scale inequalities of the classical Hardy, Pólya-Knopp, and Hardy-Hilbert. Some continuous inequalities are derived from the main results as special cases. The essential results will be proved by making use of some algebraic inequalities such as the Minkowski inequality, the refined Jensen inequality, and the Bernoulli inequality on time scales.

scholarly journals Kantorovich type operator inequalities via the Specht ratio

2004 ◽  
Vol 377 ◽  
pp. 69-81 ◽  
Author(s):  
Jun Ichi Fujii ◽  
Yuki Seo ◽  
Masaru Tominaga
Keyword(s):  
Type Operator ◽  
Operator Inequalities

Reverse Jensen-Mercer Type Operator Inequalities

2016 ◽  
Vol 31 ◽  
pp. 87-99 ◽  
Author(s):  
Ehsan Anjidani ◽  
Mohammad Reza Changalvaiy
Keyword(s):  
Hilbert Space ◽  
Selfadjoint Operator ◽  
Type Operator ◽  
Operator Inequalities ◽  
Linear Map ◽  
Positive Linear Map

Let $A$ be a selfadjoint operator on a Hilbert space $\mathcal{H}$ with spectrum in an interval $[a,b]$ and $\phi:B(\mathcal{H})\rightarrow B(\mathcal{K})$ be a unital positive linear map, where $\mathcal{K}$ is also a Hilbert space. Let $m,M\in J$ with $m

Characterization of chaotic order and its applications to furuta's type operator inequalities

1998 ◽  
Vol 43 (4) ◽  
pp. 339-349 ◽  
Author(s):  
Masatoshi Fujii ◽  
Jian Fei Jiang ◽  
Eizaburo Kamei
Keyword(s):  
Type Operator ◽  
Operator Inequalities
Sign in / Sign up

Export Citation Format

Share Document