Resolvent algorithms for system of generalized nonlinear variational inclusions and fixed point problems

被引：8

作者：

Balooee J. ^{[1
]}

机构：

[1] Department of Mathematics, Sari Branch, Islamic Azad University, Sari

来源：

Afrika Matematika | 2014年 / 25卷 / 4期

关键词：

Convergence analysis; Fixed point problem; Nearly uniformly Lipschitzian mapping; Resolvent method; System of generalized nonlinear variational inclusions;

D O I：

10.1007/s13370-013-0171-5

中图分类号：

学科分类号：

摘要：

In this paper, we consider a new system of generalized nonlinear variational inclusions involving A-maximal m-relaxed η-accretive [so-called, (A η)-accretive (Lan et al. in Comput Math Appl 51:1529–1538 2006)] mappings in q-uniformly smooth Banach spaces. By using the resolvent operator technique associated with A-maximal m-relaxed η-accretive mappings, we prove the existence of a unique solution of the aforementioned system. We use nearly uniformly Lipschitzian mappings Si(i=1,2,...,p) to define a self mapping Q =(S1, S2...,Sp). Then by using resolvent operator technique associated with A-relaxed η-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 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. © 2013, African Mathematical Union and Springer-Verlag Berlin Heidelberg.

引用

页码：1023 / 1042

页数：19

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