Measures of noncompactness in fixed point theory for monotone operators and applications

Abstract

We prove two counterparts of Darbo–Sadovskiĭ’s theorems for monotone operators $F:X\to X$ acting on an ordered metric space $X$. As applications, we show the existence of solutions for some functional-integral and ordinary differential equations. The selection of a suitable measure of noncompactness is the main tool in solving the equations. Several examples are provided to illustrate our results.