Further generalization of Walker’s inequality in acute triangles and its applications

Jian Liu; Jian Liu

doi:10.3934/math.2020428

AIMS Mathematics

2020, Volume 5, Issue 6: 6657-6672. doi: 10.3934/math.2020428

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Research article

Further generalization of Walker’s inequality in acute triangles and its applications

Jian Liu ^,

East China Jiaotong University, Nanchang, Jiangxi 330013, China

Received: 06 July 2020 Accepted: 18 August 2020 Published: 25 August 2020
MSC : 51M16

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.
- Walker’s inequality,
- Euler’s inequality,
- Ciamberlini’s inequality,
- acute (non-obtuse) triangle,
- circumradius,
- inradious,
- semiperimeter,
- non-negative real number
Citation: Jian Liu. Further generalization of Walker’s inequality in acute triangles and its applications[J]. AIMS Mathematics, 2020, 5(6): 6657-6672. doi: 10.3934/math.2020428

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Abstract

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.

References

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