New perturbed finite step iterative algorithms for a system of extended generalized nonlinear mixed quasi-variational inclusions

Authors:
M. Alimohammady;J. Balooee;Y. J. Cho;M. Roohi
Affiliations:
Department of Mathematics, Faculty of Basic Sciences, University of Mazandaran, Babolsar 47416-1468, Iran;Department of Mathematics, Faculty of Basic Sciences, University of Mazandaran, Babolsar 47416-1468, Iran;Department of Mathematics Education and the RINS, Gyeongsang National University, Chinju 660-701, Republic of Korea;Department of Mathematics, Faculty of Basic Sciences, University of Mazandaran, Babolsar 47416-1468, Iran
Venue:
Computers & Mathematics with Applications
Year:
2010

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Abstract

This paper introduces a new system of extended generalized nonlinear mixed quasi-variational inclusions involving A-maximal m-relaxed @h-accretive (so called (A,@h)-accretive (Lan et al. (2006) [37])) mappings in q-uniformly smooth Banach spaces. By using the resolvent operator technique for A-maximal m-relaxed @h-accretive mappings due to Lan et al., we establish the existence and uniqueness of solution for this system of extended generalized nonlinear mixed quasi-variational inclusions and construct a new perturbed N-step iterative algorithm with mixed errors for solving the mentioned system. We also prove the convergence of the sequences generated by our algorithms in q-uniformly smooth Banach spaces. The results presented in this paper extend and improve some known results in the literature.