In:
Creative Mathematics and Informatics, Technical University of Cluj Napoca, North University Center of Baia Mare, Vol. 31, No. 1 ( 2022-02-01), p. 109-120
Abstract:
"For q 〉 1, let E be a q-uniformly smooth real Banach space with dual space E∗. Let A : E → E∗ be a Lipschitz and strongly monotone mapping such that A^{−1}(0) ̸= ∅. For given x_1 ∈ E, let {x_n} be generated iteratively by the algorithm : x_{n+1} = x_n − λJ^{−1}(Ax_n), n ≥ 1, where J is the normalized duality mapping from E into E∗ and λ is a positive real number choosen in a suitable interval. Then it is proved that the sequence {xn} converges strongly to x∗, the unique point of A^{−1}(0). Our theorems are applied to the convex minimization problem. Futhermore, our technique of proof is of independent interest."
Type of Medium:
Online Resource
ISSN:
1584-286X
,
1843-441X
DOI:
10.37193/CMI.2022.01
DOI:
10.37193/CMI.2022.01.11
Language:
Unknown
Publisher:
Technical University of Cluj Napoca, North University Center of Baia Mare
Publication Date:
2022
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