Abstract Generalized Quasilinearization Method for Coincidences

Abstract

An abstract unified theory of both monotone iterative and generalized quasilinearization methods is presented for operator equations of coincidence type in ordered Banach spaces. Applications are given for semilinear problems in $C(\overline{\Omega};\mathbb{R}^k)$ and $L^p(\Omega;\methbb{R}^k)$.