A strong convergence theorem for generalized-Φ-strongly monotone maps, with applications
Abstract Let X be a uniformly convex and uniformly smooth real Banach space with dual space X∗ $X^{*}$. In this paper, a Mann-type iterative algorithm that approximates the zero of a generalized-Φ-strongly monotone map is constructed. A strong convergence theorem for a sequence generated by the algo...
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| Main Authors: | , , |
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| Format: | article |
| Language: | EN |
| Published: |
SpringerOpen
2019
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| Subjects: | |
| Online Access: | https://doaj.org/article/9883bb84ed6a4efba6f8d7ad52d0c74d |
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| Summary: | Abstract Let X be a uniformly convex and uniformly smooth real Banach space with dual space X∗ $X^{*}$. In this paper, a Mann-type iterative algorithm that approximates the zero of a generalized-Φ-strongly monotone map is constructed. A strong convergence theorem for a sequence generated by the algorithm is proved. Furthermore, the theorem is applied to approximate the solution of a convex optimization problem, a Hammerstein integral equation, and a variational inequality problem. This theorem generalizes, improves, and complements some recent results. Finally, examples of generalized-Φ-strongly monotone maps are constructed and numerical experiments which illustrate the convergence of the sequence generated by our algorithm are presented. |
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