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The common iterative Halpern’s type method for fixed points and equilibrium solutions of asymptotically nonexpansive mappings. (Chinese. English summary) Zbl 1449.47127

Summary: This paper studied the approximation of a common element of the set of solutions of equilibrium problems and fixed points of asymptotically nonexpansive mappings in real Hilbert spaces. By using Halpern’s type iterative algorithm, a new transformation iterative sequence was constructed. Under suitable weaker conditions, the strong convergence of the sequence was obtained. The results have a wider adaptability and include some recent results as their special cases.

MSC:

47J26 Fixed-point iterations
47H09 Contraction-type mappings, nonexpansive mappings, \(A\)-proper mappings, etc.
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