Iteratively regularized Landweber iteration method: Convergence analysis via Hölder stability

In this paper, the local convergence of Iteratively regularized Landweber iteration method is investigated for solving non-linear inverse problems in Banach spaces. Our analysis mainly relies on assumption that mapping satisfies Hölder stability estimate locally. We consider both noisy as well non-noisy data our analysis. Under a-priori choice stopping index data, we show iterates remain a certain ball around exact solution and obtain rates. The to shown under assumptions case by-product, different conditions, two rates are obtained.