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<p>An iterative method for approximating solutions of nonlinear ill-posed equations with m-accretive (in Banach space)/ monotone (in Hilbert space) operator is considered with weaker assumptions. Precisely, Lavrentiev regularization method is studied in Banach space with m-accretive operator and in Hilbert space with monotone operator. An optimal order of convergence is obtained with a new source condition and apriori parameter choice strategy as in S. George et.al., [<CitationRef CitationID="CR16">16</CitationRef>]. Numerical example is presented, which justifies the analysis.</p>

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Lavrentiev regularization of nonlinear ill-posed equations in Banach and Hilbert space

  • 期刊论文

  • 发表日期：

    2024年12月31日

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  • Shobha M. Erappa,
  • P. B. Suma

摘要

An iterative method for approximating solutions of nonlinear ill-posed equations with m-accretive (in Banach space)/ monotone (in Hilbert space) operator is considered with weaker assumptions. Precisely, Lavrentiev regularization method is studied in Banach space with m-accretive operator and in Hilbert space with monotone operator. An optimal order of convergence is obtained with a new source condition and apriori parameter choice strategy as in S. George et.al., [16]. Numerical example is presented, which justifies the analysis.