Abstract
A theorem which gives a necessary and sufficient condition for the strong convergence of the semigroup generated by an m-accretive operator defined on the whole Banach space E and of the steepest descent approximation process to a zero of a quasi-accretive operator A in Banach spaces is presented. The theorem states that the sequence generated by the steepest descent approximation process converges hyperstrongly to the element of the null space of A. This theorem is reformulated in the more general setting in which the operator is defined on a proper subset of E and takes values in E.
| Original language | English |
|---|---|
| Pages (from-to) | 81-96 |
| Number of pages | 16 |
| Journal | Nonlinear Analysis, Theory, Methods and Applications |
| Volume | 37 |
| Issue number | 1 |
| DOIs | |
| Publication status | Published - Jan 1 1999 |
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All Science Journal Classification (ASJC) codes
- Analysis
- Applied Mathematics
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Approximation of the zeros of m-accretive operators. / Chidume, C. E.; Zegeye, Habtu.
In: Nonlinear Analysis, Theory, Methods and Applications, Vol. 37, No. 1, 01.01.1999, p. 81-96.Research output: Contribution to journal › Article
TY - JOUR
T1 - Approximation of the zeros of m-accretive operators
AU - Chidume, C. E.
AU - Zegeye, Habtu
PY - 1999/1/1
Y1 - 1999/1/1
N2 - A theorem which gives a necessary and sufficient condition for the strong convergence of the semigroup generated by an m-accretive operator defined on the whole Banach space E and of the steepest descent approximation process to a zero of a quasi-accretive operator A in Banach spaces is presented. The theorem states that the sequence generated by the steepest descent approximation process converges hyperstrongly to the element of the null space of A. This theorem is reformulated in the more general setting in which the operator is defined on a proper subset of E and takes values in E.
AB - A theorem which gives a necessary and sufficient condition for the strong convergence of the semigroup generated by an m-accretive operator defined on the whole Banach space E and of the steepest descent approximation process to a zero of a quasi-accretive operator A in Banach spaces is presented. The theorem states that the sequence generated by the steepest descent approximation process converges hyperstrongly to the element of the null space of A. This theorem is reformulated in the more general setting in which the operator is defined on a proper subset of E and takes values in E.
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UR - http://www.scopus.com/inward/citedby.url?scp=0033165475&partnerID=8YFLogxK
U2 - 10.1016/S0362-546X(98)00146-1
DO - 10.1016/S0362-546X(98)00146-1
M3 - Article
VL - 37
SP - 81
EP - 96
JO - Nonlinear Analysis, Theory, Methods and Applications
JF - Nonlinear Analysis, Theory, Methods and Applications
SN - 0362-546X
IS - 1
ER -