Integral Form of Popoviciu Inequality for Convex Function: Integral Form of Popoviciu Inequality for Convex Function

Khuram Ali  Khan; Tasadduq  Niaz; Josip  Pečarić

Authors

Khuram Ali Khan Department of Mathematics, University of Sargodha, Sargodha 40100, Pakistan
Tasadduq Niaz Department of Mathematics, University of Sargodha, Sargodha 40100, Pakistan
Josip Pečarić Faculty of Textile Technology, University of Zagreb, 10000 Zagreb, Croatia

Keywords:

Convex function, Popoviciu inequality, Jensen’s inequality, quasi arithmetic means

Abstract

In this paper, the new integral form of Popoviciu inequality for convex functions is constructed and also the new refinement of integral form of Jensen’s inequality is given. For the purpose of application some new quasi arithmetic means are defined along with their monotonicity property. Keywords: Convex function, Popoviciu inequality, Jensen’s inequality, quasi arithmetic means

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Integral Form of Popoviciu Inequality for Convex Function