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arXiv · 2510.03774

H\"{o}lder property of the resolvent of a monotone operator in Banach spaces

Changchi Huang·Jigen Peng·Yuchao Tang
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Abstract

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 H\"{o}lder 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.

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Changchi Huang, Jigen Peng, Yuchao Tang. 2025-10-04. H\"{o}lder property of the resolvent of a monotone operator in Banach spaces. https://arxiv.org/abs/2510.03774

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