ACTA issues

## Some renormings of Banach spaces with the weak fixed point property for nonexpansive mappings

Gopal Dutta, P. Veeramani

Acta Sci. Math. (Szeged) 85:1-2(2019), 171-180
89/2017

 Abstract. In 2013, Jiménez--Melado and Llorens--Fuster proved that the renorming of $\ell ^2$, $|x|=\max\{\|x\|_2,p(x)\}$, where $p$ is a seminorm on $\ell ^2$ satisfying certain conditions, has the weak fixed point property. In this paper, we generalize this result for a Banach space having normal structure and Schauder basis. From this, we derive that every Banach space having normal structure and Schauder basis has an equivalent renorming that lacks asymptotic normal structure but has the weak fixed point property. DOI: 10.14232/actasm-017-339-4 AMS Subject Classification (1991): 47H09, 47H10, 46B20 Keyword(s): nonexpansive mappings, weak fixed point property Received December 30, 2017 and in final form April 28, 2018. (Registered under 89/2017.)