Some extensions of Krasnoselskii's fixed point result for real functions

Hassan Khandani

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arXiv · 2209.03247

Some extensions of Krasnoselskii's fixed point result for real functions

Hassan Khandani

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Abstract

We extend Krasnoselskii's fixed point result to non-self-real functions. We find a new and simple proof for Hillam's result. In our approach, we don't assume the image of the related mapping to be compact or bounded. In this way, we extend Hillam's result to self-mappings on $\mathbb R$. Finally, we present a new proof for the global convergence of the Newton-Raphson method.

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Hassan Khandani. 2022-09-05. Some extensions of Krasnoselskii's fixed point result for real functions. https://arxiv.org/abs/2209.03247

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