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τ-DISTANCE IN A GENERAL TOPOLOGICAL SPACE (X, τ) WITH APPLICATION TO FIXED POINT THEORY M

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Electronic Journal: Southwest Journal of Pure and Applied Mathematics Internet: http://rattler.cameron.edu/swjpam.html

ISSN 1083-0464

Issue 2, December 2003, pp. 1–5.

Submitted: April 15, 2003. Published: December 31 2003.

τ-DISTANCE IN A GENERAL TOPOLOGICAL SPACE (X, τ) WITH APPLICATION TO FIXED POINT THEORY

M. AAMRI and D. EL MOUTAWAKIL

Abstract. The main purpose of this paper is to define the notion of aτ-distance function in a general topological space (X, τ). As application, we get a generalization of the well known Banach’s fixed point theorem.

A.M.S. (MOS) Subject Classification Codes. 54A05, 47H10, 54H25, 54E70 Key Words and Phrases. Hausdorff topological spaces, Topological spaces of type F, symmetrizable topological spaces, Fixed points of contractive maps

Department of Mathematics and Informatics, University Hassan-II Mohammedia, Casablanca , Morocco

E-mail Address: d.elmoutawakil@math.net 2003 Cameron Universityc

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