Chinese Annals of Mathematics, Series B

, Volume 34, Issue 4, pp 593–622

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

Article

DOI: 10.1007/s11401-013-0777-9

Cite this article as:
Balooee, J. Chin. Ann. Math. Ser. B (2013) 34: 593. doi:10.1007/s11401-013-0777-9

Abstract

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 S1 and S2 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 = (S1, S2) 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.

Keywords

A-Maximal m-relaxed η-accretive mapping System of generalized nonlinear variational-like inclusion Resolvent operator technique Convergence and stability Variational convergence 

2000 MR Subject Classification

47H05 47H09 47J05 

Copyright information

© Fudan University and Springer-Verlag Berlin Heidelberg 2013

Authors and Affiliations

  1. 1.Department of Mathematics, Sari BranchIslamic Azad UniversitySariIran

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