Electron. J. Diff. Equ., Vol. 2009(2009), No. 117, pp. 1-15.

Mean value theorems for some linear integral operators

Cezar Lupu, Tudorel Lupu

In this article we study some mean value results involving linear integral operators on the space of continuous real-valued functions defined on the compact interval [0,1]. The existence of such points will rely on some classical theorems in real analysis like Rolle, Flett and others. Our approach is rather elementary and does not use advanced techniques from functional analysis or nonlinear analysis.

Submitted June 18, 2009. Published September 24, 2009.
Math Subject Classifications: 26A24, 26A33, 26E20.
Key Words: Integral operators; mean value theorem.

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Cezar Lupu
University of Bucharest, Faculty of Mathematics, Str.
Academiei 14, 70109 Bucharest, Romania
email: lupucezar@yahoo.com, lupucezar@gmail.com
Tudorel Lupu
"Decebal" High School, Department of Mathematics
Aleea Gradinitei 4, 900478 Constanta, Romania
email: tudorellupu@yahoo.com, tudorellupu@gmail.com

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