Strong convergence theorems for modifying Halpern iterations for quasi-\(\phi\)-asymptotically nonexpansive multivalued mapping in Banach spaces with applications. (English) Zbl 1263.47083

Summary: An iterative sequence for quasi-\(\phi\)-asymptotically nonexpansive multivalued mapping for modifying Halpern’s iterations is introduced. Under suitable conditions, some strong convergence theorems are proved. The results presented in the paper improve and extend the corresponding results in the work by S.-S. Chang et al. [Appl. Math. Comput. 217, No. 18, 7520–7530 (2011; Zbl 1221.65132)].


47J25 Iterative procedures involving nonlinear operators
47H09 Contraction-type mappings, nonexpansive mappings, \(A\)-proper mappings, etc.
47H04 Set-valued operators


Zbl 1221.65132
Full Text: DOI


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