WEAK AND STRONG CONVERGENCE FOR QUASI-NONEXPANSIVE MAPPINGS IN BANACH SPACES

- Journal title : Bulletin of the Korean Mathematical Society
- Volume 49, Issue 4, 2012, pp.799-813
- Publisher : The Korean Mathematical Society
- DOI : 10.4134/BKMS.2012.49.4.799

Title & Authors

WEAK AND STRONG CONVERGENCE FOR QUASI-NONEXPANSIVE MAPPINGS IN BANACH SPACES

Kim, Gang-Eun;

Kim, Gang-Eun;

Abstract

In this paper, we first show that the iteration {} defined by converges strongly to some fixed point of T when E is a real uniformly convex Banach space and T is a quasi-nonexpansive non-self mapping satisfying Condition A, which generalizes the result due to Shahzad [11]. Next, we show the strong convergence of the Mann iteration process with errors when E is a real uniformly convex Banach space and T is a quasi-nonexpansive self-mapping satisfying Condition A, which generalizes the result due to Senter-Dotson [10]. Finally, we show that the iteration {} defined by converges strongly to a common fixed point of T and S when E is a real uniformly convex Banach space and T, S are two quasi-nonexpansive self-mappings satisfying Condition D, which generalizes the result due to Ghosh-Debnath [3].

Keywords

weak and strong convergence;fixed point;Opial's condition;Condition A;Condition D;quasi-nonexpansive mapping;

Language

English

Cited by

1.

2.

References

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