Fixed point iteration for a countable family of multi-valued strictly pseudo-contractive-type mappings

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• 作者：C. E. Chidume ; M. E. Okpala
• 关键词：Generalized k ; strictly pseudo ; contractive multi ; valued mappings ; Multi ; valued maps ; 47H04 ; 47H09 ; 47H10
• 刊名：SpringerPlus
• 出版年：2015
• 出版时间：December 2015
• 年：2015
• 卷：4
• 期：1
• 全文大小：1818KB
• 参考文献：Abbas M, Khan SH, Khan AR, Agarwal RP (2011) Common fixed points of two multi-valued nonexpansive mappings by onestep iterative scheme. Appl Math Lett 24(2):97102CrossRef
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• 作者单位：C. E. Chidume (1) (2)
  M. E. Okpala (2)
  
  1. Mathematics Institute, African University of Sciences and Technology, Abuja, Nigeria
  2. Department of Mathematics, Federal University Ndufu-Alike Ikwo, Abakaliki, Ebonyi State, Nigeria
  
• 刊物类别：Science, general;
• 刊物主题：Science, general;
• 出版者：Springer International Publishing
• ISSN：2193-1801

文摘

This paper introduces a new averaged algorithm for finding a common fixed point of a countably infinite family of generalized k-strictly pseudocontractive multi-valued mappings. The new iterative sequence introduced is proved to be an approximating fixed point sequence for common fixed points of a countably infinite family of this class of mappings. Furthermore, under some mild assumptions, strong convergence theorems are also proved for this class of mappings. The method of proof used here is new and enables to overcome many strong restrictions appearing in contemporary literature. The stated theorems improve and generalize many recent works in iterative scheme for multi-valued mappings. Keywords Generalized k-strictly pseudo-contractive multi-valued mappings Multi-valued maps