Entropy results for Levinson-type inequalities via Green functions and Hermite interpolating polynomial

2021 ◽  
Author(s):  
Muhammad Adeel ◽  
Khuram Ali Khan ◽  
Đilda Pečarić ◽  
Josip Pečarić
Keyword(s):  
Green Functions ◽  
Hermite Interpolating Polynomial

scholarly journals New bounds for Shannon, Relative and Mandelbrot entropies via Hermite interpolating polynomial

2018 ◽  
Vol 51 (1) ◽  
pp. 112-130
Author(s):  
Nasir Mehmood ◽  
Saad Ihsan Butt ◽  
Ðilda Pečarić ◽  
Josip Pečarić
Keyword(s):  
Applied Sciences ◽  
Information Theory ◽  
Convex Function ◽  
Error Term ◽  
Probability Distributions ◽  
Jensen’S Inequality ◽  
Higher Order ◽  
Green Functions ◽  
Jensen's Inequality ◽  
Hermite Interpolating Polynomial

AbstractTo procure inequalities for divergences between probability distributions, Jensen’s inequality is the key to success. Shannon, Relative and Zipf-Mandelbrot entropies have many applications in many applied sciences, such as, in information theory, biology and economics, etc. We consider discrete and continuous cyclic refinements of Jensen’s inequality and extend them from convex function to higher order convex function by means of different new Green functions by employing Hermite interpolating polynomial whose error term is approximated by Peano’s kernal. As an application of our obtained results, we give new bounds for Shannon, Relative and Zipf-Mandelbrot entropies.

scholarly journals Bulk-Boundary Correspondence for Non-Hermitian Hamiltonians via Green Functions

2021 ◽  
Vol 126 (21) ◽  
Author(s):  
Heinrich-Gregor Zirnstein ◽  
Gil Refael ◽  
Bernd Rosenow
Keyword(s):  
Green Functions ◽  
Boundary Correspondence

Green functions for confined quarks

1976 ◽  
Vol 109 (3) ◽  
pp. 421-438 ◽  
Author(s):  
C.J. Hamer
Keyword(s):  
Green Functions

scholarly journals Levinson-type inequalities via new Green functions and Montgomery identity

2020 ◽  
Vol 18 (1) ◽  
pp. 632-652 ◽  
Author(s):  
Muhammad Adeel ◽  
Khuram Ali Khan ◽  
Ðilda Pečarić ◽  
Josip Pečarić
Keyword(s):  
Convex Functions ◽  
Green Functions ◽  
Montgomery Identity ◽  
Data Points

Abstract In this study, Levinson-type inequalities are generalized by using new Green functions and Montgomery identity for the class of k-convex functions (k ≥ 3). Čebyšev-, Grüss- and Ostrowski-type new bounds are found for the functionals involving data points of two types. Moreover, a new functional is introduced based on {\mathfrak{f}} divergence and then some estimates for new functional are obtained. Some inequalities for Shannon entropies are obtained too.

Integrals of the motion, green functions, and coherent states of dynamical systems

1975 ◽  
Vol 14 (1) ◽  
pp. 37-54 ◽  
Author(s):  
V. V. Dodonov ◽  
I. A. Malkin ◽  
V. I. Man'ko
Keyword(s):  
Dynamical Systems ◽  
Coherent States ◽  
Green Functions

scholarly journals Theory of Green functions of free Dirac fermions in graphene

2016 ◽  
Vol 7 (1) ◽  
pp. 015013
Author(s):  
Van Hieu Nguyen ◽  
Bich Ha Nguyen ◽  
Ngoc Dung Dinh
Keyword(s):  
Green Functions ◽  
Dirac Fermions

Green functions of scalar particles in stochastic fields

1989 ◽  
Vol 28 (12) ◽  
pp. 1463-1482 ◽  
Author(s):  
M. Dineykhan ◽  
G. V. Efimov ◽  
Kh. Namsrai
Keyword(s):  
Green Functions ◽  
Scalar Particles ◽  
Stochastic Fields
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