Iterative algorithm with mixed errors for solving a new system of generalized nonlinear variational-like inclusions and fixed point problems in Banach spaces

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• 作者：Javad Balooee (1777)
  
• 关键词：A ; Maximal m ; relaxed η ; accretive mapping ; System of generalized nonlinear variational ; like inclusion ; Resolvent operator technique ; Convergence and stability ; Variational convergence ; 47H05 ; 47H09 ; 47J05
• 刊名：Chinese Annals of Mathematics - Series B
• 出版年：2013
• 出版时间：July 2013
• 年：2013
• 卷：34
• 期：4
• 页码：593-622
• 全文大小：369KB
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• 作者单位：Javad Balooee (1777)
  
  1777. Department of Mathematics, Sari Branch, Islamic Azad University, Sari, Iran
  

文摘

A new system of generalized nonlinear variational-like inclusions involving A-maximal m-relaxed η-accretive (so-called, (A, η)-accretive in [36]) mappings in q-uniformly smooth Banach spaces is introduced, and then, by using the resolvent operator technique associated with A-maximal m-relaxed η-accretive mappings due to Lan et al., the existence and uniqueness of a solution to the aforementioned system is established. Applying two nearly uniformly Lipschitzian mappings S 1 and S 2 and using the resolvent operator technique associated with A-maximal m-relaxed η-accretive mappings, we shall construct a new perturbed N-step iterative algorithm with mixed errors for finding an element of the set of the fixed points of the nearly uniformly Lipschitzian mapping Q = (S 1, S 2) which is the unique solution of the aforesaid system. We also prove the convergence and stability of the iterative sequence generated by the suggested perturbed iterative algorithm under some suitable conditions. The results presented in this paper extend and improve some known results in the literature.