Demiclosedness principle and convergence theorems for strictly pseudocontractive mappings of Browder-Petryshyn type

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS

卷:256

Article

Osilike, MO ; Udomene, A

关键词: fixed points;    strictly pseudocontractive maps;    Mann iteration;    Ishikawa iteration;   

DOI  :  10.1006/jmaa.2000.7257

来源: Elsevier

【 摘 要 】

Let E be a red q-uniformly smooth Banach space which is also uniformly convex (for example, L-p or l(p), spaces, 1 < infinity) and K a nonempty closed convex subset of E. Let T: K --> K be a strictly pseudocontractive mapping in the sense of F. E. Browder and W. V. Petryshyn (1967, J. Math. Anal. Appl. 20, 197-228). It is proved that (I - T) is demiclosed at zero. If P(T) = {x is an element of K: Tx = x} not equal null set, weak and strong convergence of the Mann and Ishikawa iteration methods to a fixed point of T is proved. (C) 2001 Academic Press.

【 授权许可】

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