A new fixed point theorem in the fractal space

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• 作者：Song-il Ri ^{si1974730@163.com" class="auth_mail" title="E-mail the corresponding author}
• 关键词：Fixed points ; Generalized contraction ; Hausdorff distance ; Fractal ; Topological equivalent
• 刊名：Indagationes Mathematicae
• 出版年：2016
• 出版时间：January 2016
• 年：2016
• 卷：27
• 期：1
• 页码：85-93
• 全文大小：169 K

文摘

In this paper we present some important generalizations of the Banach contraction principle in which the Lipschitz constant class="mathmlsrc">class="formulatext stixSupport mathImg" data-mathURL="/science?_ob=MathURL&_method=retrieve&_eid=1-s2.0-S0019357715000592&_mathId=si1.gif&_user=111111111&_pii=S0019357715000592&_rdoc=1&_issn=00193577&md5=9a3f1dfe71ddf2838e2d67f9675133cf" title="Click to view the MathML source">kclass="mathContainer hidden">class="mathCode">$k$ is replaced by some real-valued control function.

For the applications to the fractal, we obtain the fixed point theorem of the some generalized contraction in the fractal space.