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

Yi, Li

J. Appl. Math. 2012, Article ID 912545, 11 p. (2012).

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)].

MSC:

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

Keywords:

iterative algorithm; quasi-\(\phi\)-asymptotically nonexpansive multivalued mapping; modified Halpern iteration; strong convergence

Citations:

Zbl 1221.65132

References:

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