Iterative algorithm with mixed errors for solving a new system of generalized nonlinear variationallike inclusions and fixed point problems in Banach spaces
 Javad Balooee
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A new system of generalized nonlinear variationallike inclusions involving Amaximal mrelaxed ηaccretive (socalled, (A, η)accretive in [36]) mappings in quniformly smooth Banach spaces is introduced, and then, by using the resolvent operator technique associated with Amaximal mrelaxed ηaccretive 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 Amaximal mrelaxed ηaccretive mappings, we shall construct a new perturbed Nstep 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.
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 Title
 Iterative algorithm with mixed errors for solving a new system of generalized nonlinear variationallike inclusions and fixed point problems in Banach spaces
 Journal

Chinese Annals of Mathematics, Series B
Volume 34, Issue 4 , pp 593622
 Cover Date
 20130701
 DOI
 10.1007/s1140101307779
 Print ISSN
 02529599
 Online ISSN
 18606261
 Publisher
 Springer Berlin Heidelberg
 Additional Links
 Topics
 Keywords

 AMaximal mrelaxed ηaccretive mapping
 System of generalized nonlinear variationallike inclusion
 Resolvent operator technique
 Convergence and stability
 Variational convergence
 47H05
 47H09
 47J05
 Authors

 Javad Balooee ^{(1777)}
 Author Affiliations

 1777. Department of Mathematics, Sari Branch, Islamic Azad University, Sari, Iran