An Induction Theorem and Nonlinear Regularity Models
An Induction Theorem and Nonlinear Regularity Models
A general nonlinear regularity model for a set-valued mapping $F:X\times\mathbb{R}_+\rightrightarrows Y$, where $X$ and $Y$ are metric spaces, is studied using special iteration procedures, going back to Banach, Schauder, Lyusternik, and Graves. Namely, we revise the induction theorem from Khanh [J. Math. Anal. Appl., 118 (1986), pp. 519--534] and employ …