Fixed points of Mizoguchi-Takahashi contraction on a metric space with a graph and applications

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• 作者：Asrifa Sultana ; V. Vetrivel ; ^{vetri@iitm.ac.in" class="auth_mail}
• 关键词：Fixed point ; Multi-valued map ; Graph ; Metric space ; 蔚-chainable metric space
• 刊名：Journal of Mathematical Analysis and Applications
• 出版年：1 September, 2014
• 年：2014
• 卷：417
• 期：1
• 页码：336-344
• 全文大小：266 K

文摘

In this paper we extend Mizoguchi-Takahashi's fixed point theorem for multi-valued mappings on a metric space endowed with a graph. As an application, we establish a fixed point theorem on an 蔚-chainable metric space for mappings satisfying Mizoguchi-Takahashi contractive condition uniformly locally. Also, we establish a result on the convergence of successive approximations for certain operators (not necessarily linear) on a Banach space as another application. Consequently, this result yields the Kelisky-Rivlin theorem on iterates of the Bernstein operators on the space and also enables us study the asymptotic behaviour of iterates of some nonlinear Bernstein type operators on .