A Krasnosel’skii–Zincenko-type method in $$K\!$$ K -normed spaces for solving equations

Abstract

We present a new semilocal convergence result for a Krasnosel’skii–Zincenko-type method (KZTM) to solve a nonlinear operator equation in a \(K\!\)-normed space setting. Using our new idea of restricted convergence domains, we show how to expand the convergence domain of KZTM under the same computational cost as in earlier studies. Numerical examples show how to solve an equation in cases not possible before.