Abstract
By using a new technique, namely, a specific way of choosing the indexes of the involved mappings, we introduce a new iterative algorithm for approximating common fixed points of a countable family of multi-valued totally quasi-ϕ-asymptotically nonexpansive mappings and obtain a strong convergence theorem under some suitable conditions. As application, an iterative solution to a system of generalized mixed equilibrium problems is studied. The results extend those of other authors, in which the involved mapping consists of just a single one.
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This work is supported by the National Natural Science Foundation of China (Grant No.11061037).
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Deng, WQ. A new iterative algorithm for solving a system of generalized mixed equilibrium problems for a kind of multi-valued nonlinear mappings. Numer Algor 66, 779–791 (2014). https://doi.org/10.1007/s11075-013-9762-3
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DOI: https://doi.org/10.1007/s11075-013-9762-3
Keywords
- System of generalized mixed equilibrium problems
- Totally quasi-ϕ-asymptotically nonexpansive multi-valued mappings
- Generalized projections