A sufficient and necessary condition for the convergence of the sequence of successive approximations to a unique fixed point期刊界 All Journals 搜尽天下杂志传播学术成果专业期刊搜索期刊信息化学术搜索

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A sufficient and necessary condition for the convergence of the sequence of successive approximations to a unique fixed point

Authors:	Tomonari Suzuki

Institution:	Department of Mathematics, Kyushu Institute of Technology, Sensuicho, Tobata, Kitakyushu 804-8550, Japan

Abstract:	If is a complete metric space and $T : X \to X$ is a contraction mapping, then the conclusion of the Banach-Caccioppoli contraction principle is that the sequence of successive approximations of starting from any point of the space converges to a unique fixed point. In this paper, we obtain a sufficient and necessary condition of the above conclusion in terms of the so-called strong Leader mappings.

Keywords:	Fixed point successive approximations Banach-Caccioppoli contraction principle Leader mapping

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