George, S.Sreedeep, C.D.Argyros, I.K.2026-02-042023Journal of Inverse and Ill-Posed Problems, 2023, 31, 1, pp. 147-1579280219https://doi.org/10.1515/jiip-2021-0019https://idr.nitk.ac.in/handle/123456789/22060In this paper, we study secant-type iteration for nonlinear ill-posed equations involving m-accretive mappings in Banach spaces. We prove that the proposed iterative scheme has a convergence order at least 2.20557 using assumptions only on the first Fréchet derivative of the operator. Further, using a general Hölder-type source condition, we obtain an optimal error estimate. We also use the adaptive parameter choice strategy proposed by Pereverzev and Schock (2005) for choosing the regularization parameter. © 2022 Walter de Gruyter GmbH, Berlin/Boston 2023.Nonlinear equationsParameterization47h0647j0547j0649j3065j20Adaptive parameter choice strategyAdaptive parametersIterative schemesLavrentiev regularizationsNonlinear ill-posed problemsParameter choiceSecant-type iterative schemeBanach spaces