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

作者：Balooee Javad^*

来源：Chinese Annals of Mathematics Series B, 2013, 34(4): 593-622.

DOI：10.1007/s11401-013-0777-9

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

A new system of generalized nonlinear variational-like inclusions involving A-maximal m-relaxed eta-accretive (so-called, (A, eta)-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 eta-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 S (1) and S (2) and using the resolvent operator technique associated with A-maximal m-relaxed eta-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 = (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.

• 出版日期2013-7