Iterative approximation of endpoints for multivalued mappings in Banach spaces. (English) Zbl 1467.47024
Summary: The purpose of this paper is to introduce the modified Agarwal-O’Regan-Sahu iteration process (S-iteration) for finding endpoints of multivalued nonexpansive mappings in the setting of Banach spaces. Under suitable conditions, some weak and strong convergence results of the iterative sequence generated by the proposed process are proved. Our results especially improve and unify some recent results of B. Panyanak [J. Fixed Point Theory Appl. 20, No. 2, Paper No. 77, 8 p. (2018; Zbl 1465.47051)]. At the end of the paper, we offer an example to illustrate the main results.
MSC:
| 47J25 | Iterative procedures involving nonlinear operators |
| 47H04 | Set-valued operators |
| 47H09 | Contraction-type mappings, nonexpansive mappings, \(A\)-proper mappings, etc. |
Citations:
Zbl 1465.47051References:
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