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

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.

Keywords

• walker’s inequality
• euler’s inequality
• ciamberlini’s inequality
• acute (non-obtuse) triangle
• circumradius
• inradious
• semiperimeter
• non-negative real number