Fixed points for mappings of asymptotically nonexpansive type
Departamento de Análisis Matemático, Universidad de Sevilla, Tarfia s/n, 41012-Sevilla, Spain, E-mail: [email protected], T. Domínguez Benavides, Lorenzo Ramírez P., Departamento de Análisis Matemático, Universidad de Sevilla, Tarfia s/n, 41012-Sevilla, Spain, E-mail: [email protected] · Fixed Point Theory · 2023
We prove the existence of fixed points for mappings which satisfy some asymptotic nonexpansive conditions in Banach spaces which are either nearly uniformly convex or they satisfy that asymptotic centers of bounded sequences are compact.Nominally, we consider pointwise eventually nonexpansive mappings, pointwise asymptotically nonexpansive mappings and asymptotically type nonexpansive mappings.We do not assume the existence of a continuous iterate, solving some longstanding open questions about existence of a fixed point for these mappings in absence of continuity [7].