Geodesic
Generalizations of some Hardy-Littlewood-Pólya type inequalities and related results
Filomat, Tome 35 (2021) no. 8, p. 2811

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DOI

In this paper, we use an identity of Fink and present some interesting identities and inequalities for real valued functions and r-convex functions respectively. We also obtain generalizations of some Hardy-Littlewood-Pólya type inequalities. In addition, we use the Čebyšev functional and the Grüss type inequalities and find the bounds for the remainder in the obtained identities. Finally, we present an interesting result related to the Ostrowski type inequalities
DOI : 10.2298/FIL2108811K
Classification : 26A51, 26D15
Keywords: Non-increasing sequence in weighted mean, Hardy-Littlewood-Pólya inequality, Shannon entropy, Fink’s identity, r-convex function, Čebyšev functional, Grüss and Ostrowski type inequalities 
Sadia Khalid; Josip Pečarić. Generalizations of some Hardy-Littlewood-Pólya type inequalities and related results. Filomat, Tome 35 (2021) no. 8, p. 2811 . doi: 10.2298/FIL2108811K
@article{10_2298_FIL2108811K,
     author = {Sadia Khalid and Josip Pe\v{c}ari\'c},
     title = {Generalizations of some {Hardy-Littlewood-P\'olya} type inequalities and related results},
     journal = {Filomat},
     pages = {2811 },
     year = {2021},
     volume = {35},
     number = {8},
     doi = {10.2298/FIL2108811K},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.2298/FIL2108811K/}
}
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