n-exponential convexity of some dynamic Hardy-type functionals

2014 ◽  
pp. 331-347 ◽  
Author(s):  
Khuram Ali Khan ◽  
Ammara Nosheen ◽  
Josip Pečarić
Keyword(s):  
Exponential Convexity ◽  
Hardy Type

scholarly journals Hardy-Type Inequalities for an Extension of the Riemann- Liouville Fractional Derivative Operators

2021 ◽  
Vol 45 (5) ◽  
pp. 797-813
Author(s):  
SAJID IQBAL ◽  
◽  
GHULAM FARID ◽  
JOSIP PEČARIĆ ◽  
ARTION KASHURI
Keyword(s):  
Fractional Derivative ◽  
Convex Functions ◽  
Mean Value ◽  
Mean Value Theorems ◽  
Hardy Type Inequalities ◽  
Exponential Convexity ◽  
Hardy Type ◽  
Liouville Fractional Derivative ◽  
Fractional Derivative Operators

In this paper we present variety of Hardy-type inequalities and their refinements for an extension of Riemann-Liouville fractional derivative operators. Moreover, we use an extension of extended Riemann-Liouville fractional derivative and modified extension of Riemann-Liouville fractional derivative using convex and monotone convex functions. Furthermore, mean value theorems and n-exponential convexity of the related functionals is discussed.

Multidimensional reversed Hardy type inequalities for monotone functions

2014 ◽  
Vol 07 (04) ◽  
pp. 1450055
Author(s):  
Saad Ihsan Butt ◽  
Josip Pečarić ◽  
Ivan Perić ◽  
Marjan Praljak
Keyword(s):  
Mean Value ◽  
Monotone Functions ◽  
Mean Value Theorems ◽  
Hardy Type Inequalities ◽  
Multidimensional Generalization ◽  
Exponential Convexity ◽  
Hardy Type ◽  
Cauchy Means

In this paper, we will give some multidimensional generalization of reversed Hardy type inequalities for monotone functions. Moreover, we will give n-exponential convexity, exponential convexity and related results for some functionals obtained from the differences of these inequalities. At the end we will give mean value theorems and Cauchy means for these functionals.

scholarly journals n-Exponential Convexity of Hardy-type and Boas-type functionals

2013 ◽  
pp. 739-750
Author(s):  
Sajid Iqbal ◽  
Kristina Krulić Himm lreich ◽  
Josip Pečarić ◽  
Dora Pokaz
Keyword(s):  
Exponential Convexity ◽  
Hardy Type

scholarly journals Hardy-type estimates for Dirac operators

2007 ◽  
Vol 40 (6) ◽  
pp. 885-900 ◽  
Author(s):  
J DOLBEAULT ◽  
M ESTEBAN ◽  
J DUOANDIKOETXEA ◽  
L VEGA
Keyword(s):  
Dirac Operators ◽  
Hardy Type

scholarly journals Experimental test of the Greenberger–Horne–Zeilinger-type paradoxes in and beyond graph states

2021 ◽  
Vol 7 (1) ◽  
Author(s):  
Zheng-Hao Liu ◽  
Jie Zhou ◽  
Hui-Xian Meng ◽  
Mu Yang ◽  
Qiang Li ◽  
...  
Keyword(s):  
Quantum Mechanics ◽  
Quantum Theory ◽  
Success Probability ◽  
Quantum Foundations ◽  
Mixed States ◽  
Graph States ◽  
Hardy Type ◽  
Realistic Description ◽  
Entanglement Detection ◽  
Quantum Paradoxes

AbstractThe Greenberger–Horne–Zeilinger (GHZ) paradox is an exquisite no-go theorem that shows the sharp contradiction between classical theory and quantum mechanics by ruling out any local realistic description of quantum theory. The investigation of GHZ-type paradoxes has been carried out in a variety of systems and led to fruitful discoveries. However, its range of applicability still remains unknown and a unified construction is yet to be discovered. In this work, we present a unified construction of GHZ-type paradoxes for graph states, and show that the existence of GHZ-type paradox is not limited to graph states. The results have important applications in quantum state verification for graph states, entanglement detection, and construction of GHZ-type steering paradox for mixed states. We perform a photonic experiment to test the GHZ-type paradoxes via measuring the success probability of their corresponding perfect Hardy-type paradoxes, and demonstrate the proposed applications. Our work deepens the comprehension of quantum paradoxes in quantum foundations, and may have applications in a broad spectrum of quantum information tasks.

scholarly journals On a weighted inequality of Hardy type in spaces Lp(⋅)

2009 ◽  
Vol 353 (2) ◽  
pp. 521-530 ◽  
Author(s):  
Farman I. Mamedov ◽  
Aziz Harman
Keyword(s):  
Weighted Inequality ◽  
Hardy Type

scholarly journals Some new Hardy-type inequalities on time scales

2020 ◽  
Vol 2020 (1) ◽  
Author(s):  
Ahmed A. El-Deeb ◽  
Hamza A. Elsennary ◽  
Dumitru Baleanu
Keyword(s):  
Time Scales ◽  
Hardy Type Inequalities ◽  
Hardy Type

scholarly journals Pseudo-monotonicity and degenerated or singular elliptic operators

1998 ◽  
Vol 58 (2) ◽  
pp. 213-221 ◽  
Author(s):  
P. Drábek ◽  
A. Kufner ◽  
V. Mustonen
Keyword(s):  
Sobolev Spaces ◽  
Differential Operators ◽  
Weighted Sobolev Spaces ◽  
Type Inequality ◽  
Elliptic Operators ◽  
Hardy Type Inequality ◽  
Hardy Type ◽  
Elliptic Differential Operators

Using the compactness of an imbedding for weighted Sobolev spaces (that is, a Hardy-type inequality), it is shown how the assumption of monotonicity can be weakened still guaranteeing the pseudo-monotonicity of certain nonlinear degenerated or singular elliptic differential operators. The result extends analogous assertions for elliptic operators.

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