Wang, Yuanheng; Chen, Lingfa The common iterative Halpern’s type method for fixed points and equilibrium solutions of asymptotically nonexpansive mappings. (Chinese. English summary) Zbl 1449.47127 J. Zhejiang Norm. Univ., Nat. Sci. 42, No. 2, 121-128 (2019). 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. Keywords:asymptotically nonexpansive mappings; equilibrium problem; fixed point; Halpern’s type iteration; strong convergence PDFBibTeX XMLCite \textit{Y. Wang} and \textit{L. Chen}, J. Zhejiang Norm. Univ., Nat. Sci. 42, No. 2, 121--128 (2019; Zbl 1449.47127) Full Text: DOI