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| Volume 7, Number 2, August 2006, pp. 289-297 | |||||||||
| Zead Mustafa and Brailey Sims | |||||||||
| Key words: | |||||||||
| metric space, generalized metric space, D-metric space, 2-metric space | |||||||||
| Mathematices Subject Classification: Primary 47H10, Secondary 46B20 | |||||||||
|
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| Volume 7, Number 2, August 2006, pp. 289-297 | |||||||||
| Zead Mustafa and Brailey Sims | |||||||||
| Key words: | |||||||||
| metric space, generalized metric space, D-metric space, 2-metric space | |||||||||
| Mathematices Subject Classification: Primary 47H10, Secondary 46B20 | |||||||||
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| Abstract: | |||
| 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) |
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| A new approach to generalized metric spaces | |||