Resolvent algorithms for system of generalized nonlinear variational inclusions and fixed point problems
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- 作者：Javad Balooee (1)
- 关键词：System of generalized nonlinear variational inclusions ; Nearly uniformly Lipschitzian mapping ; Fixed point problem ; Resolvent method ; Convergence analysis ; 47H05 ; 47J20 ; 47J22 ; 49J40 ; 90C33
- 刊名：Afrika Matematika
- 出版年：2014
- 出版时间：December 2014
- 年：2014
- 卷：25
- 期：4
- 页码：1023-1042
- 全文大小：277 KB
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文摘
In this paper, we consider a new system of generalized nonlinear variational inclusions involving \(A\) -maximal \(m\) -relaxed \(\eta \) -accretive [so-called, \((A,\eta )\) -accretive (Lan et al. in Comput Math Appl 51:1529-538 2006)] mappings in \(q\) -uniformly smooth Banach spaces. By using the resolvent operator technique associated with \(A\) -maximal \(m\) -relaxed \(\eta \) -accretive mappings, we prove the existence of a unique solution of the aforementioned system. We use nearly uniformly Lipschitzian mappings \(S_i\) \((i=1,2,\ldots ,p)\) to define a self mapping \(\mathcal Q =(S_1,S_2,\ldots ,S_p)\) . Then by using resolvent operator technique associated with \(A\) -maximal \(m\) -relaxed \(\eta \) -accretive mappings, we shall construct a \(p\) -step iterative algorithm with mixed errors for finding an element of the set of the fixed points of \(\mathcal Q \) which is also a unique solution of the aforesaid system. We also establish the convergence of the iterative sequence generated by the proposed algorithm under some suitable conditions. The results presented in this paper extend and improve several known results in the literature.