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

Document Type: Research Paper


1 Department of Mathematics, Mashhad Branch, Islamic Azad University,mashhad, Iran

2 School of Mathematics, Iran University of Science and Technology, Narmark, Tehran 16846 13114, Iran


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.