scholarly journals Estimation of f-divergence and Shannon entropy by Levinson type inequalities via new Green’s functions and Lidstone polynomial

2020 ◽  
Vol 2020 (1) ◽  
Author(s):  
Muhammad Adeel ◽  
Khuram Ali Khan ◽  
Ðilda Pečarić ◽  
Josip Pečarić
Keyword(s):  
Shannon Entropy ◽  
Green's Functions ◽  
Green’S Functions ◽  
Lidstone Polynomial

scholarly journals Refinements of some Hardy–Littlewood–Pólya type inequalities via Green’s functions and Fink’s identity and related results

2020 ◽  
Vol 2020 (1) ◽  
Author(s):  
Sadia Khalid ◽  
Josip Pečarić
Keyword(s):  
Shannon Entropy ◽  
Convex Functions ◽  
Green's Functions ◽  
Green’S Functions ◽  
Hölder’S Inequality ◽  
Hölder's Inequality ◽  
Čebyšev Functional ◽  
Grüss Type Inequalities ◽  
Fink’S Identity

AbstractIn this paper, first we present some interesting identities associated with Green’s functions and Fink’s identity, and further we present some interesting inequalities for r-convex functions. We also present refinements of some Hardy–Littlewood–Pólya type inequalities and give an application to the Shannon entropy. Furthermore, we use the Čebyšev functional and Grüss type inequalities and present the bounds for the remainder in the obtained identities. Finally, we use the obtained identities together with Hölder’s inequality for integrals and present Ostrowski type inequalities.

Temperature field evaluation of a two-dimensional partial heat flow problem through Green's Functions

2019 ◽  
Author(s):  
Guilherme Ramalho Costa ◽  
José Aguiar santos junior ◽  
José Ricardo Ferreira Oliveira ◽  
Jefferson Gomes do Nascimento ◽  
Gilmar Guimaraes
Keyword(s):  
Temperature Field ◽  
Heat Flow ◽  
Green's Functions ◽  
Flow Problem ◽  
Green’S Functions ◽  
Field Evaluation ◽  
Two Dimensional
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