**Jian Liu**

East China Jiaotong University, Nanchang 330013, China; liujian999@ecjtu.jx.cn

Received: 10 July 2019; Accepted: 5 August 2019; Published: 9 August 2019

**Abstract:** In this paper, two new refinements of the Erdös–Mordell inequality and three new refinements of Barrow's inequality are established. Some related interesting conjectures are put forward.

**Keywords:** Erdös–Mordell inequality; Barrow's inequality; triangle; interior point
