| Ishikawa Iterative Process with Errors for Lipschitzian and φ-Hemicontractive Mappings in Banach Spaces |
| Received:October 10, 1997 Revised:August 30, 1999 |
| Key Words:
Ishikawa iteration with errors φ-strongly quasi-accretive mapping φ-hemicontraction arbitrary Banach space.
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| Abstract: |
| Let X be a real Banish space, K a nonempty convex subset of X such that K + K?K. Let T: K → K be a Lipschitzian andφ-hemicontractive mapping with a Lipschitzian constant L ≥ 1. Let {αn}∞n=0, and {βn}∞n=0 be two real sequences in [0, 1] satisfying: (i) αn→0,βn→ 0 as n → ∞; (ii) (?)αn=∞ . Assume that {un}∞n=0 and {vn}∞n=0 are two sequences in K satisfying . ‖un‖= o(αn),vn → 0 as n →∞. For an arbitrary xn∈K define a sequence {xn}∞n=0 in K by(?) If {Tyn} is bounded, then the sequence {xn} converges strongly to the unique fixed point of T. A related result deals with iterative solution of nonlinear equations with φ-strongly quasi-accretive mappings by the Ishikawa iteration with errors in an arbitrary Banach space. |
| Citation: |
| DOI:10.3770/j.issn:1000-341X.2000.02.001 |
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