On the Measure of Noncompactness in Banach Spaces and Application to the Theory of Differential and Integral Equations

This chapter deals with measure of noncompactness (briefly MNC) in Banach spaces and application to the theory of differential and integral equations. We review some important generalizations of Darbo’s theorem and we provide sufficient conditions for extension of this theorem for two commuting operators. Also, by making use of the proved theorems, we consider the existence and behaviour of solutions of integral and differential equations with feedback control.