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<p>We present a new fixed point result in Banach spaces by using divided differences of first order and auxiliary points to obtain a result of the so-called restricted fixed point. In particular, we use the secant method to draw conclusions about the fixed point and the domain where it is located, so that we obtain global convergence of the secant method to approximate the fixed point with superlinear speed of convergence.</p>

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A Fixed-Point Result in Banach Spaces from Divided Differences

  • 期刊论文

  • 出版模式：

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  • 发表日期：

    2025年1月19日

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  • J. A. Ezquerro,
  • M. A. Hernández-Verón

摘要

We present a new fixed point result in Banach spaces by using divided differences of first order and auxiliary points to obtain a result of the so-called restricted fixed point. In particular, we use the secant method to draw conclusions about the fixed point and the domain where it is located, so that we obtain global convergence of the secant method to approximate the fixed point with superlinear speed of convergence.