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

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

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...

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Veröffentlicht in:International journal of analysis 2015-01, Vol.2015, p.1-4
1. Verfasser: Mihai, Monea
Format: Artikel
Sprache:eng
Schlagworte:
Integrals
Proving
Stability
Theorems
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Beschreibung
Zusammenfassung: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.
ISSN:2314-498X
2314-4998
DOI:10.1155/2015/894625