Convex functions and inequalities in the secondary school
Articles
Juozas Šinkūnas
Vilniaus pedagoginis universitetas
Published 2008-12-21
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Keywords

function
convex function
arithmetic
geometric
harmonic and quadraticmeans
trigonometric and geometric inequalities

How to Cite

Šinkūnas J. (2008) “Convex functions and inequalities in the secondary school”, Lietuvos matematikos rinkinys, 48(proc. LMS), pp. 142–148. Available at: https://www.journals.vu.lt/LMR/article/view/18081 (Accessed: 9August2022).

Abstract

A function f : DR is called convex if for any x, y Df the inequality f ( x+y/2 ) \leq (f (x)+f (y)  )/2 holds. We prove the main property of the convex fonctions (inequality (4)) and also the inequalities which the arithmetic, geometric, harmonic and quadratic means of several positive numbers satisfy. Then we prove some trigonometric and geometric inequalities. 

     

 

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