An Integral Mean Value Theorem concerning Two Continuous Functions and Its Stability | Zendy

‎Mihai Monea | Zendy

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An Integral Mean Value Theorem concerning Two Continuous Functions and Its Stability

Author(s) -

‎Mihai Monea

Publication year - 2015

Publication title -

international journal of analysis

Language(s) - English

Resource type - Journals

eISSN - 2314-4998

pISSN - 2314-498X

DOI - 10.1155/2015/894625

Subject(s) - mathematics , mean value theorem (divided differences) , counterexample , stability (learning theory) , fundamental theorem of calculus , fixed point theorem , stability theorem , value (mathematics) , fundamental theorem , mean value , discrete mathematics , mathematical economics , pure mathematics , calculus (dental) , picard–lindelöf theorem , mathematical analysis , statistics , computer science , medicine , dentistry , machine learning , cauchy distribution

The aim of this paper is to investigate an integral mean value theorem proposed by one of the references of this paper. Unfortunately, the proof contains a gap. First, we present a counterexample which shows that this theorem fails in this form. Then, we present two improved versions of this theorem. The stability of the mean point arising from the second result concludes this paper

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