Convergence analysis of iterative sequences for a pair of mappings in Banach spaces |
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| Authors: | Liu Chuan Zeng N C Wong J C Yao |
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| Institution: | (1) Department of Mathematics, Shanghai Normal University, Shanghai, 200234, P. R. China;(2) Department of Applied Mathematics, National Sun Yat-Sen University, Kaohsiung, Taiwan, 80424, China |
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| Abstract: | Let C be a nonempty closed convex subset of a real Banach space E. Let S: C → C be a quasi-nonexpansive mapping, let T: C → C be an asymptotically demicontractive and uniformly Lipschitzian mapping, and let F:= {x ε C: Sx = x and Tx = x} ≠ 0. Let {x
n
}
n≥0 be the sequence generated from an arbitrary x
0 ε C by We prove the necessary and sufficient conditions for the strong convergence of the iterative sequence {x
n
} to an element of F. These extend and improve the recent results of Moore and Nnoli.
This research is partially supported by the Teaching and Research Award Fund for Outstanding Young Teachers in Higher Education
Institutions of MOE, China and the Dawn Program Foundation in Shanghai and partially supported by grant from the National
Science Council of Taiwan |
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| Keywords: | quasi-nonexpansive mapping asymptotically demicontractive type mapping iterative sequence convergence analysis |
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