Local convergence analysis of frozen Steffensen-type methods under generalized conditions

Abstract

The goal in this study is to present a unified local convergence analysis of frozen Steffensen-type methods under generalized Lipschitz-type conditions for Banach space valued operators. We also use our new idea of restricted convergence domains, where we find a more precise location, where the iterates lie leading to at least as tight majorizing functions. Consequently, the new convergence criteria are weaker than in earlier works resulting to the expansion of the applicability of these methods. The conditions do not necessarily imply the differentiability of the operator involved. This way our method is suitable for solving equations and systems of equations.

Keywords

• Banach space
• frozen Steffensen-type method
• local convergence
• generalized Lipschitz conditions