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Secant-type iteration for nonlinear ill-posed equations in Banach space

  • Santhosh George ORCID logo , C. D. Sreedeep ORCID logo EMAIL logo and Ioannis K. Argyros ORCID logo
Published/Copyright: January 4, 2022

Abstract

In 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.

MSC 2010: 47J06; 47J05; 65J20; 47H06; 49J30

Award Identifier / Grant number: 020111/17/2020

Funding statement: The work of Santhosh George is supported by National Board of Higher Mathematics (NBHM), No. 020111/17/2020 NBHM (R.P.)/R & D II/8073.

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Received: 2019-11-29
Revised: 2021-10-01
Accepted: 2021-10-22
Published Online: 2022-01-04
Published in Print: 2023-02-01

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