Geodesic
Upper and lower estimations of Popoviciu's difference via weighted Hadamard inequality with applications
Filomat, Tome 37 (2023) no. 22, p. 7641

Voir la notice de l'article provenant de la source eLibrary of Mathematical Institute of the Serbian Academy of Sciences and Arts

DOI

We consider differences coming from Popoviciu's inequality and give upper and lower bounds by employing weighted Hermite-Hadamard inequality along with the approximations of Montgomery two point formula. We also give bounds for Popoviciu's inequality by employing weighted Hermite-Hadamard inequality along with the approximations of Montgomery one point formula. We testify this scenario by utilizing the theory of n-times differentiable convex functions. Our results hold for all n ≥ 2 and we provide explicit examples to show the correctness of the bounds obtained for special cases. Last but not least, we provide applications in information theory by providing new uniform estimations of the generalized Csiszár divergence, Rényi-divergence, Shannon-entropy, Kullback-Leibler divergence, Zipf and Hybrid Zipf-Mandelbrot entropies.
DOI : 10.2298/FIL2322641B
Classification : 26A51, 41A10, 26D15, 94A17
Keywords: Popoviciu’s inequality, Montgomery identity, Weighted Hermite-Hadamard inequality, Shannon-Entropy, Kullback-Leibler distance, Zipf and Hybrid-Zipf Law 
S I Butt; T Rasheed; Ð Pečarić; J Pečarić. Upper and lower estimations of Popoviciu's difference via weighted Hadamard inequality with applications. Filomat, Tome 37 (2023) no. 22, p. 7641 . doi: 10.2298/FIL2322641B
@article{10_2298_FIL2322641B,
     author = {S I Butt and T Rasheed and {\DH} Pe\v{c}ari\'c and J Pe\v{c}ari\'c},
     title = {Upper and lower estimations of {Popoviciu's} difference via weighted {Hadamard} inequality with applications},
     journal = {Filomat},
     pages = {7641 },
     year = {2023},
     volume = {37},
     number = {22},
     doi = {10.2298/FIL2322641B},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.2298/FIL2322641B/}
}
TY  - JOUR
AU  - S I Butt
AU  - T Rasheed
AU  - Ð Pečarić
AU  - J Pečarić
TI  - Upper and lower estimations of Popoviciu's difference via weighted Hadamard inequality with applications
JO  - Filomat
PY  - 2023
SP  - 7641 
VL  - 37
IS  - 22
UR  - http://geodesic.mathdoc.fr/articles/10.2298/FIL2322641B/
DO  - 10.2298/FIL2322641B
LA  - en
ID  - 10_2298_FIL2322641B
ER  - 
%0 Journal Article
%A S I Butt
%A T Rasheed
%A Ð Pečarić
%A J Pečarić
%T Upper and lower estimations of Popoviciu's difference via weighted Hadamard inequality with applications
%J Filomat
%D 2023
%P 7641 
%V 37
%N 22
%U http://geodesic.mathdoc.fr/articles/10.2298/FIL2322641B/
%R 10.2298/FIL2322641B
%G en
%F 10_2298_FIL2322641B

Cité par Sources :