General Approximation-Solvability of Nonlinear Equations Involving $\mathcal{A}$-regular Operators

Abstract

Here we consider a general approximation-solvability scheme involving $\mathcal{A}$-regular operators - a generalization of $\mathcal{A}$-proper operators - introduced and studied by Petryshyn [4] and further studied by Milojevic’ [3], Petryshyn [6] and others. Among significant applications, an $\mathcal{A}$-regular version of the Petryshyn theorem is given.