Fixed points by certain iterative schemes with applications

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• 作者：Ahmed El-Sayed Ahmed (1) (2)
  Sayed Attia Ahmed (3) (4)
  
  1. Department of Mathematics ; Faculty of Science ; Sohag University ; Sohag ; 82524 ; Egypt
  2. Mathematics Department ; Faculty of Science ; Taif University ; El-Hawiyah ; P.O. Box 888 ; El-Taif ; 5700 ; Saudi Arabia
  3. Department of Mathematics ; Faculty of Science ; Assiut University ; Assiut ; Egypt
  4. Department of Mathematics ; University College ; Umm Al-Qura University ; Mecca ; Saudi Arabia
  
• 关键词：fixed points ; Hilbert spaces ; Mann iteration ; pseudo ; contractive maps ; weakly compatible maps
• 刊名：Fixed Point Theory and Applications
• 出版年：2014
• 出版时间：December 2014
• 年：2014
• 卷：2014
• 期：1
• 全文大小：203 KB
• 参考文献：1. Berinde, V (2007) Lecture Notes in Mathematics 1912. Iterative Approximation of Fixed Points. Springer, Berlin
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• 刊物主题：Analysis; Mathematics, general; Applications of Mathematics; Differential Geometry; Topology; Mathematical and Computational Biology;
• 出版者：Springer International Publishing
• ISSN：1687-1812

文摘

The main aim of this paper is to present the concept of general Mann and general Ishikawa type double-sequences iterations with errors to approximate fixed points. We prove that the general Mann type double-sequence iteration process with errors converges strongly to a coincidence point of two continuous pseudo-contractive mappings, each of which maps a bounded closed convex nonempty subset of a real Hilbert space into itself. Moreover, we discuss equivalence from the -stabilities point of view under certain restrictions between the general Mann type double-sequence iteration process with errors and the general Ishikawa iterations with errors. An application is also given to support our idea using compatible-type mappings. MSC: 47H10, 54H25.