Argyros, I.K.George, S.2020-03-312020-03-312019Panamerican Mathematical Journal, 2019, Vol.29, 2, pp.93-103https://idr.nitk.ac.in/handle/123456789/9549We present a new semi-local convergence analysis for an inverse free Broyden-type Banach to Hilbert space scheme (BTS) in order to approximate a locally unique solution of an equation. The analysis is based on a center-Lipschitz-type condition and our idea of the restricted convergence region. The operators involved have regularly continuous divided differences. This way we provide, weaker sufficient semi-local convergence conditions, tighter error bounds, and a more precise information on the location of the solution. Hence, our approach extends the applicability of BTS under the same hypotheses as before. 2019, International Publications. All rights reserved.Article