A UNIFIED GENERALIZATION OF ACZEL, POPOVICIU AND BELLMAN'S INEQUALITIES

被引：4
|
作者：
Wu, Shanhe [1 ]
机构：
[1] Longyan Univ, Dept Math & Comp Sci, Longyan 364012, Fujian, Peoples R China
来源：
TAIWANESE JOURNAL OF MATHEMATICS | 2010年 / 14卷 / 04期
关键词：
Aczel's inequality; Popoviciu's inequality; Bellman's inequality; Power mean; Generalization; Refinement; IMPROVEMENTS;
D O I：
10.11650/twjm/1500405974
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
In this paper, we give a unified generalization of Aczel, Popoviciu and Bellman's inequalities. The result is then applied to deriving a refinement of Aczel's inequality and Bellman's inequality. As consequences, several interesting integral inequalities of Aczel-Popoviciu-Bellman type are obtained.
引用
收藏
页码：1635 / 1646
页数：12
相关论文
共 50 条
  • [41] On Cerone's and Bellman's generalization of Steffensen's integral inequality via conformable sense
    El-Khatib, Mohammed S.
    Abu Hany, Atta A. K.
    Matar, Mohammed M.
    Alqudah, Manar A.
    Abdeljawad, Thabet
    AIMS MATHEMATICS, 2022, 8 (01): : 2062 - 2082
  • [42] Popoviciu's Inequality Again
    Bojaxhiu, Elton
    Hysnelaj, Enkel
    AMERICAN MATHEMATICAL MONTHLY, 2010, 117 (01): : 88 - 89
  • [43] A Generalization of Newton-Maclaurin's Inequalities
    Ren, Changyu
    INTERNATIONAL MATHEMATICS RESEARCH NOTICES, 2024, 2024 (05) : 3799 - 3822
  • [44] A generalization of Maclaurin's inequalities and its applications
    Pecaric, J
    Wen, JJ
    Wang, WL
    Lu, T
    MATHEMATICAL INEQUALITIES & APPLICATIONS, 2005, 8 (04): : 583 - 598
  • [45] On Maz'ya's Φ-Inequalities for Martingale Fractional Integration and Their Bellman Functions
    Stolyarov, Dmitriy
    MICHIGAN MATHEMATICAL JOURNAL, 2024, 74 (03) : 509 - 526
  • [46] Extensions and Applications of Power-Type Aczel-Vasic-Pecaric's Inequalities
    Chen, Kun
    Yan, Fei
    Yue, Hong-Ying
    MATHEMATICAL PROBLEMS IN ENGINEERING, 2019, 2019
  • [47] WEIGHTED POPOVICIU TYPE INEQUALITIES VIA GENERALIZED MONTGOMERY IDENTITIES
    Butt, Saad Ihsan
    Pecaric, Josip
    RAD HRVATSKE AKADEMIJE ZNANOSTI I UMJETNOSTI-MATEMATICKE ZNANOSTI, 2015, 19 (523): : 69 - 89
  • [48] An Application of Popoviciu's Inequality
    Tetiva, Marian
    AMERICAN MATHEMATICAL MONTHLY, 2009, 116 (08): : 752 - 753
  • [49] REVERSED VERSIONS OF ACZEL-TYPE INEQUALITY AND BELLMAN-TYPE INEQUALITY
    Tian, Jing-Feng
    Wang, Wen-Li
    JOURNAL OF MATHEMATICAL INEQUALITIES, 2015, 9 (02): : 417 - 424
  • [50] New Bellman-Type Inequalities
    Pashaei, R.
    Asgari, M. S.
    JOURNAL OF MATHEMATICAL EXTENSION, 2021, 15 (04)
12345