Fixed point and stability results for multi-valued nonlinear graph contractions in complete metric spaces

Abstract In this work we will present a generalization of Covitz-Nadler’s contraction principle, as well as of the multi-valued graph contraction principle. The results of this paper extend and complement well-known fixed point theorems. Also, several stability properties are proved. In the last section, a Maia type theorem for a multi-valued nonlinear graph contraction is proved. An application to an integral inclusion of the Volterra type is given.