Some extensions of Darbo's theorem and solutions of integral equations of Hammerstein type

In this brief note,  using the technique of measures of noncompactness, we give some extensions of Darbo fixed point theorem. Also we prove  an existence result for a quadratic  integral equation of Hammerstein type on an unbounded interval in two variables  which includes several classes of nonlinear integral equations of Hammerstein type. Furthermore, an example is presented to show the efficiency of our result.

Keywords:

Measure of noncompactness , Quadratic integral equation , Darbo fixed point theorem