Jensen Functional, Quasi-Arithmetic Mean and Sharp Converses of Holder's Inequalities
Апстракт
In this article, we give sharp two-sided bounds for the generalized Jensen functional J(n)(f,g,h;p,x). Assuming convexity/concavity of the generating function h, we give exact bounds for the generalized quasi-arithmetic mean A(n)(h;p,x). In particular, exact bounds are determined for the generalized power means in terms from the class of Stolarsky means. As a consequence, some sharp converses of the famous Holder's inequality are obtained.
Кључне речи:
quasi-arithmetic means / power means / Holder's inequality / convex functionsИзвор:
Mathematics, 2021, 9, 23Издавач:
- MDPI, Basel
Финансирање / пројекти:
- Faculty of Organizational Sciences, University of Belgrade, Serbia [11143]
DOI: 10.3390/math9233104
ISSN: 2227-7390
WoS: 000735077800001
Scopus: 2-s2.0-85120790384
Институција/група
Fakultet organizacionih naukaTY - JOUR AU - Simić, Slavko AU - Todorčević, Vesna PY - 2021 UR - https://rfos.fon.bg.ac.rs/handle/123456789/2163 AB - In this article, we give sharp two-sided bounds for the generalized Jensen functional J(n)(f,g,h;p,x). Assuming convexity/concavity of the generating function h, we give exact bounds for the generalized quasi-arithmetic mean A(n)(h;p,x). In particular, exact bounds are determined for the generalized power means in terms from the class of Stolarsky means. As a consequence, some sharp converses of the famous Holder's inequality are obtained. PB - MDPI, Basel T2 - Mathematics T1 - Jensen Functional, Quasi-Arithmetic Mean and Sharp Converses of Holder's Inequalities IS - 23 VL - 9 DO - 10.3390/math9233104 UR - conv_2592 ER -
@article{ author = "Simić, Slavko and Todorčević, Vesna", year = "2021", abstract = "In this article, we give sharp two-sided bounds for the generalized Jensen functional J(n)(f,g,h;p,x). Assuming convexity/concavity of the generating function h, we give exact bounds for the generalized quasi-arithmetic mean A(n)(h;p,x). In particular, exact bounds are determined for the generalized power means in terms from the class of Stolarsky means. As a consequence, some sharp converses of the famous Holder's inequality are obtained.", publisher = "MDPI, Basel", journal = "Mathematics", title = "Jensen Functional, Quasi-Arithmetic Mean and Sharp Converses of Holder's Inequalities", number = "23", volume = "9", doi = "10.3390/math9233104", url = "conv_2592" }
Simić, S.,& Todorčević, V.. (2021). Jensen Functional, Quasi-Arithmetic Mean and Sharp Converses of Holder's Inequalities. in Mathematics MDPI, Basel., 9(23). https://doi.org/10.3390/math9233104 conv_2592
Simić S, Todorčević V. Jensen Functional, Quasi-Arithmetic Mean and Sharp Converses of Holder's Inequalities. in Mathematics. 2021;9(23). doi:10.3390/math9233104 conv_2592 .
Simić, Slavko, Todorčević, Vesna, "Jensen Functional, Quasi-Arithmetic Mean and Sharp Converses of Holder's Inequalities" in Mathematics, 9, no. 23 (2021), https://doi.org/10.3390/math9233104 ., conv_2592 .