On Regular Operator Approximation Theory

In this paper the approximation-solvability of nonlinear operator equations involving φ-pseudo-monotone operators and their compact perturbations is considered not by the projection methods, but by a more general method of regular operator approximation theory-an improvement over the usual convergence method of approximate solutions in the sense that it yields the convergence of approximate solutions under minimal hypotheses. First, we obtain results in a Hilbert space setting and then upgrade them to the case of reflexive Banach spaces. Finally, an application is considered.