Hölder property of the resolvent of a monotone operator in Banach spaces

2025/10/04 by Huang, Changchi, Peng, Jigen, Tang, Yuchao
#46B20 #47H05 #47H10 #FOS: Mathematics #Functional Analysis (math.FA)

paper · doi:10.48550/arxiv.2510.03774

Abstract

Let E be a Banach space, and let J: E → 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

Citations

• Metric and Generalized Projection Operators in Banach Spaces: Properties\n and Applications

Related

• On α-monotone operators and their resolvent in Banach spaces
• General Resolvents for Monotone Operators: Characterization and Extension
• Maximal monotonicity, conjugation and the duality product in non-reflexive Banach spaces
• Representation formulas for maximal monotone operators of type (D) in Banach spaces whose dual spaces are strictly convex
• A duality operators/Banach spaces