An iterative solution to a system of nonlinear Hammerstein type equations and a system of generalized mixed equilibrium problems

作者：Deng, Wei-Qi^*

来源：Journal of Fixed Point Theory and Applications, 2017, 19(3): 2051-2068.

DOI：10.1007/s11784-016-0389-6

• System of Hammerstein type equations
• system of generalized mixed equilibrium problems
• totally quasi-phi-asymptotically nonexpansive mappings

A useful iteration method for the approximation of common fixed points of countable families of nonlinear mappings is applied, by which an iterative algorithm is presented for finding common elements of the set of solutions to a system of generalized mixed equilibrium problems, of null spaces of a countable family of -inverse strongly monotone mappings, and of the set of common fixed points of a countable family of totally quasi--asymptotically nonexpansive mappings. A strong convergence theorem is established in the framework of two-uniformly convex and uniformly smooth real Banach spaces. Since there is no need to impose uniformity assumption on the involved mappings and no need to compute series at each step in the iteration process, the results improve and extend those announced by most authors with related researches. As application, an iterative solution to a system of nonlinear Hammerstein type equations is studied.

• 出版日期2017-9
• 单位云南财经大学