A new approach to generalized metric spaces 论文

详细信息

发表日期

2006-08-01

发表年份

2006

摘要

To overcome fundamental flaws in B. C. Dhage's theory of generalized metric spaces, flaws that invalidate most of the results claimed for these spaces, we introduce an alternative more robust generalization of metric spaces. Namely, that of a G-metric space, where the G-metric satisfies the axioms: (1) G(x, y, z) = 0 if x = y = z; (2) 0 < G(x, x, y) ; whenever x =/= y, (3) G(x, x, y) <= G(x, y, z) whenever z =/= y, (4) G is a symmetric function of its three variables, and (5) G(x, y, z) <= G(x, a, a) + G(a, y, z).