Hölder property of the resolvent of a monotone operator in Banach spaces
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arXiv
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| Format: | Preprint |
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2025
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| _version_ | 1866908577014218752 |
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| author | Huang, Changchi Peng, Jigen Tang, Yuchao |
| author_facet | Huang, Changchi Peng, Jigen Tang, Yuchao |
| contents | Let $E$ be a Banach space, and let $J: E \to E^{*}$ denote the normalized duality mapping. In this paper, we establish an upper bound for $\|Jx - Jy\|$ in $q$-uniformly smooth Banach spaces, where the bound is expressed in terms of a relatively simple function of $\|x - y\|$. Subsequently, we derive the Hölder property of mappings of firmly nonexpansive type in 2-uniformly convex and $q$-uniformly smooth Banach spaces ($1<q\leq 2$). As an application,
we apply this result to the resolvent of a monotone operator in Banach spaces. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2510_03774 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Hölder property of the resolvent of a monotone operator in Banach spaces Huang, Changchi Peng, Jigen Tang, Yuchao Functional Analysis 47H10, 47H05, 46B20 Let $E$ be a Banach space, and let $J: E \to E^{*}$ denote the normalized duality mapping. In this paper, we establish an upper bound for $\|Jx - Jy\|$ in $q$-uniformly smooth Banach spaces, where the bound is expressed in terms of a relatively simple function of $\|x - y\|$. Subsequently, we derive the Hölder property of mappings of firmly nonexpansive type in 2-uniformly convex and $q$-uniformly smooth Banach spaces ($1<q\leq 2$). As an application, we apply this result to the resolvent of a monotone operator in Banach spaces. |
| title | Hölder property of the resolvent of a monotone operator in Banach spaces |
| topic | Functional Analysis 47H10, 47H05, 46B20 |
| url | https://arxiv.org/abs/2510.03774 |