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A new approach to generalized metric spaces

Mustafa, Zead and Sims, Brailey (2006) A new approach to generalized metric spaces. Journal of Nonlinear and Convex Analysis, 7 (2). pp. 289-297. ISSN 1345-4773

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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).

    Item Type: Article
    Uncontrolled Keywords: Metric space, generalized metric space, D-metric space, 2-metric space.
    Subjects: 46-xx Functional analysis > 46Bxx Normed linear spaces and Banach spaces; Banach lattices
    47-xx Operator theory > 47Hxx Nonlinear operators and their properties
    Faculty: UNSPECIFIED
    Depositing User: Mr Christopher Maitland
    Date Deposited: 07 Apr 2011 10:42
    Last Modified: 13 Apr 2011 14:26
    URI: https://docserver.carma.newcastle.edu.au/id/eprint/854

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