Abstract. A geometric approach of Blundon's inequality is presented. Theorem 2.1 gives the formula for cos ION in terms of the symmetric invariants s , R , r of a triangle, implying Blundon's inequality (Theorem 2.2). A dual formula for cos I a ON a is given in Theorem 3.1 and this implies the dual Blundon's inequality (Theorem 3.2). As applications, some inequalities involving the exradii of the triangle are presented in the last section.Mathematics subject classification (2010): 26D05; 26D15; 51N35..
In this paper, we will continue our investigation on the new recently introduced; where α is a Riemannian metric; β is a 1-form, and a ∈ 1 4 , +∞ is a real positive scalar. We will investigate the deformation of this metric, and we will investigate its properties.
Abstract. In this paper we will consider Jordan type inequalities involving hyperbolic trigonometric functions.Mathematics subject classification (2010): 26D05, 33B10.
Abstract.A geometric approach to the improvement of Blundon's inequalites given in [11] is presented. If φ = min{|A − B|,|B −C|,|C − A|}, then we proved the inequality − cos φ cos ION cos φ , where O is the circumcenter, I is the incenter, and N is the Nagel point of triangle ABC . As a direct consequence, we obtain a sharp version to Gerretsen's inequalities [7].Mathematics subject classification (2010): 26D05, 26D15, 51N35.
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