摘要
In the present work, using Minkowski functionals in topological vector spaces, we establish the equivalence between some fixed point results in metric and in (topological vector space) cone metric spaces. Thus, a lot of results in the cone metric setting can be directly obtained from their metric counterparts. In particular, a common fixed point theorem for f-quasicontractions is obtained. Our approach is even easier than that of Du [Wei-Shih Du, A note on cone metric fixed point theory and its equivalence, Nonlinear Anal. 72 (2010) 2259-2261] where similar conclusions were obtained using scalarization functions.
- 出版日期2011-3