Approximating Curves for Nonexpansive and Monotone Operators

A classical tool in nonlinear analysis is the notion of an approximating curve, whereby a particular solution to a nonuniquely solvable problem is obtained as the limit of the solutions to uniquely solvable perturbed problems. We introduce and analyze new types of approximating curves for nonexpansive fixed point problems and monotone inclusion problems in Hilbert spaces. The solution attained by these curves solves a strictly monotone variational inequality over the original solution set. Various special cases are discussed.