Fixed point theorems in locally convex spaces and a nonlinear integral equation of mixed type

*Correspondence: [email protected] School of Mathematics and Physics, Changzhou University, Changzhou, Jiangsu 213164, China Abstract In this paper, we provide a new approach for discussing the solvability of a class of operator equations by establishing fixed point theorems in locally convex spaces. Our results are obtained extend some Krasnosel’skii type fixed point theorems. As an application, we investigate the existence and global attractivity of solutions for a general nonlinear integral equation of mixed type of Urysohn and Volterra.