On Mean Value Theorems for Some Linear Integral Operators

The title of the post is the title of my undergraduate thesis. There's a long story behind it. There are problems that I have encounter upon completing the paper, but I made it. Thank God I have lots of inspirations.

The paper is all about value theorems. As a sneak peak, here's it's abstract,

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

The whole thesis can be seen here! Enjoy reading.