Electronic Journal of Differential Equations,
Vol. 2009(2009), No. 117, pp. 1-15.

Title: Mean value theorems for some linear integral operators

Authors: Cezar Lupu (Univ. of Bucharest, Romania)
         Tudorel Lupu ("Decebal" High School, Romania)

Abstract:
 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.