An Optimal Carleman-Type Inequality for the Dirac Operator

1990 ◽  
pp. 71-94 ◽  
Author(s):  
Anne Boutet de Monvel-Berthier
Keyword(s):  
Dirac Operator ◽  
Type Inequality ◽  
Carleman Type

scholarly journals Note on weighted Carleman-type inequality

2005 ◽  
Vol 2005 (3) ◽  
pp. 475-481 ◽  
Author(s):  
Chao-Ping Chen ◽  
Wing-Sum Cheung ◽  
Feng Qi
Keyword(s):  
Type Inequality ◽  
Arithmetic Mean ◽  
Logarithmic Mean ◽  
Double Inequality ◽  
Carleman Type

A double inequality involving the constanteis proved by using an inequality between the logarithmic mean and arithmetic mean. As an application, we generalize the weighted Carleman-type inequality.

scholarly journals The Hijazi Inequalities on Complete RiemannianSpincManifolds

2011 ◽  
Vol 2011 ◽  
pp. 1-14
Author(s):  
Roger Nakad
Keyword(s):  
Dirac Operator ◽  
Essential Spectrum ◽  
Finite Volume ◽  
Energy Momentum Tensor ◽  
Type Inequality ◽  
Momentum Tensor ◽  
Kato Inequality ◽  
Additional Assumptions

We extend the Hijazi type inequality, involving the energy-momentum tensor, to the eigenvalues of the Dirac operator on complete Riemannian Spincmanifolds without boundary and of finite volume. Under some additional assumptions, using the refined Kato inequality, we prove the Hijazi type inequality for elements of the essential spectrum. The limiting cases are also studied.

A Carleman Type Inequality for Sugeno Integrals

2013 ◽  
Vol 694-697 ◽  
pp. 2874-2876 ◽  
Author(s):  
Yun Xin Ma ◽  
Tian Fen Guo
Keyword(s):  
Type Inequality ◽  
Carleman Type ◽  
Points Of View

One of the famous mathematical inequalities is Carlemans inequality. It is an important inequality from both mathematical and application points of view. In this paper, a Carleman type inequality for Sugeno integrals is studied.

Lyapunov-type inequality for nonlinear systems with Riemann-Liouville fractional derivatives

2019 ◽  
Vol 49 (2) ◽  
pp. 17-34 ◽  
Author(s):  
Alireza Ansari ◽  
Shiva Eshaghi ◽  
Reza Khoshsiar Ghaziani
Keyword(s):  
Nonlinear Systems ◽  
Fractional Derivatives ◽  
Type Inequality ◽  
Lyapunov Type Inequality

On the equicontinuity of families of inverse mappings of Riemannian manifolds

2019 ◽  
Vol 16 (4) ◽  
pp. 557-566
Author(s):  
Denis Ilyutko ◽  
Evgenii Sevost'yanov
Keyword(s):  
Riemannian Manifolds ◽  
Type Inequality ◽  
The Given ◽  
Range Of Values

We study homeomorphisms of Riemannian manifolds with unbounded characteristic such that the inverse mappings satisfy the Poletsky-type inequality. It is established that their families are equicontinuous if the function Q which is related to the Poletsky inequality and is responsible for a distortion of the modulus, is integrable in the given domain, here the original manifold is connected and the domain of definition and the range of values of mappings have compact closures.

New generalized 2D Ostrowski type inequalities on time scales with k2 points using a parameter

Filomat ◽  
2018 ◽  
Vol 32 (9) ◽  
pp. 3155-3169 ◽  
Author(s):  
Seth Kermausuor ◽  
Eze Nwaeze
Keyword(s):  
Numerical Analysis ◽  
Time Scales ◽  
Type Inequality ◽  
Dimensional Case ◽  
Multiple Points ◽  
Quantum Calculus ◽  
Independent Variables ◽  
Ostrowski Type Inequality ◽  
Two Independent Variables

Recently, a new Ostrowski type inequality on time scales for k points was proved in [G. Xu, Z. B. Fang: A Generalization of Ostrowski type inequality on time scales with k points. Journal of Mathematical Inequalities (2017), 11(1):41-48]. In this article, we extend this result to the 2-dimensional case. Besides extension, our results also generalize the three main results of Meng and Feng in the paper [Generalized Ostrowski type inequalities for multiple points on time scales involving functions of two independent variables. Journal of Inequalities and Applications (2012), 2012:74]. In addition, we apply some of our theorems to the continuous, discrete, and quantum calculus to obtain more interesting results in this direction. We hope that results obtained in this paper would find their place in approximation and numerical analysis.

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