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| Iterative Algorithm with Mixed Errors for Solving a New System of Generalized Nonlinear Variational-Like Inclusions and Fixed Point Problems in Banach Spaces |
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Citation： |
Javad BALOOEE.Iterative Algorithm with Mixed Errors for Solving a New System of Generalized Nonlinear Variational-Like Inclusions and Fixed Point Problems in Banach Spaces[J].Chinese Annals of Mathematics B,2013,34(4):593~622 |
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Net amount： 1283 |
Authors： |
Javad BALOOEE; |
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| Abstract： |
A new system of generalized nonlinear variational-like inclusions involving Amaximal
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 |
Classification： |
47H05, 47H09, 47J05 |
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