Displaying similar documents to “An inequality for arithmetic and harmonic means.”

Some mean value theorems as consequences of the Darboux property

Dan Ştefan Marinescu, Mihai Monea (2017)

Mathematica Bohemica

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The aim of the paper is to present some mean value theorems obtained as consequences of the intermediate value property. First, we will prove that any nonextremum value of a Darboux function can be represented as an arithmetic, geometric or harmonic mean of some different values of this function. Then, we will present some extensions of the Cauchy or Lagrange Theorem in classical or integral form. Also, we include similar results involving divided differences. The paper was motivated...