Further generalization of Walker’s inequality in acute triangles and its applications
In this paper, we prove a generalization of Walker’s inequality in acute (non-obtuse) triangles by using Euler’s inequality, Ciamberlini’s inequality and a result due to the author, from which a number of corollaries are obtained. We also present three conjectured inequalities involving sides of an...
| Main Author: | |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
AIMS Press
2020-09-01
|
| Series: | AIMS Mathematics |
| Subjects: | |
| Online Access: | https://www.aimspress.com/article/10.3934/math.2020428/fulltext.html |
| id |
doaj-9e1e767e0df64803a68273fbd3900fbb |
|---|---|
| record_format |
Article |
| spelling |
doaj-9e1e767e0df64803a68273fbd3900fbb2020-11-25T03:05:55ZengAIMS PressAIMS Mathematics2473-69882020-09-01566657667210.3934/math.2020428Further generalization of Walker’s inequality in acute triangles and its applicationsJian Liu0East China Jiaotong University, Nanchang, Jiangxi 330013, ChinaIn this paper, we prove a generalization of Walker’s inequality in acute (non-obtuse) triangles by using Euler’s inequality, Ciamberlini’s inequality and a result due to the author, from which a number of corollaries are obtained. We also present three conjectured inequalities involving sides of an acute (non-obtuse) triangle and one exponent as open problems.https://www.aimspress.com/article/10.3934/math.2020428/fulltext.htmlwalker’s inequalityeuler’s inequalityciamberlini’s inequalityacute (non-obtuse) trianglecircumradiusinradioussemiperimeternon-negative real number |
| collection |
DOAJ |
| language |
English |
| format |
Article |
| sources |
DOAJ |
| author |
Jian Liu |
| spellingShingle |
Jian Liu Further generalization of Walker’s inequality in acute triangles and its applications AIMS Mathematics walker’s inequality euler’s inequality ciamberlini’s inequality acute (non-obtuse) triangle circumradius inradious semiperimeter non-negative real number |
| author_facet |
Jian Liu |
| author_sort |
Jian Liu |
| title |
Further generalization of Walker’s inequality in acute triangles and its applications |
| title_short |
Further generalization of Walker’s inequality in acute triangles and its applications |
| title_full |
Further generalization of Walker’s inequality in acute triangles and its applications |
| title_fullStr |
Further generalization of Walker’s inequality in acute triangles and its applications |
| title_full_unstemmed |
Further generalization of Walker’s inequality in acute triangles and its applications |
| title_sort |
further generalization of walker’s inequality in acute triangles and its applications |
| publisher |
AIMS Press |
| series |
AIMS Mathematics |
| issn |
2473-6988 |
| publishDate |
2020-09-01 |
| description |
In this paper, we prove a generalization of Walker’s inequality in acute (non-obtuse) triangles by using Euler’s inequality, Ciamberlini’s inequality and a result due to the author, from which a number of corollaries are obtained. We also present three conjectured inequalities involving sides of an acute (non-obtuse) triangle and one exponent as open problems. |
| topic |
walker’s inequality euler’s inequality ciamberlini’s inequality acute (non-obtuse) triangle circumradius inradious semiperimeter non-negative real number |
| url |
https://www.aimspress.com/article/10.3934/math.2020428/fulltext.html |
| work_keys_str_mv |
AT jianliu furthergeneralizationofwalkersinequalityinacutetrianglesanditsapplications |
| _version_ |
1724676447065341952 |