CATEGORICAL SEMANTICS OF METRIC SPACES AND CONTINUOUS LOGIC

In 1930 Kuratowski introduced the measure of non-compactness for complete metric spaces in order to measure the discrepancy a set may have from being compact.Since then several variants and generalizations concerning quanti .cation of topological and uniform properties have been studied.The introduction of approach uniform spaces,establishes a unifying setting which allows for a canonical quanti .cation of uniform concepts,such as completeness,which is the subject of this article.

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Common Fixed Point Results for Three Maps in Cone Metric Spaces

SOP Transactions on Applied Mathematics ◽

10.15764/am.2014.03005 ◽

2014 ◽

Vol 1 (3) ◽

pp. 42-47

Author(s):

K. Prudhvi ◽

Keyword(s):

Fixed Point ◽

Common Fixed Point ◽

Metric Spaces ◽

Cone Metric Spaces ◽

Cone Metric

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Some Common Fixed Point Theorem in Complete Metric Space of Integral Type

International Journal of Emerging Research in Management and Technology ◽

10.23956/ijermt.v6i8.155 ◽

2018 ◽

Vol 6 (8) ◽

pp. 297

Author(s):

Jagdish C. Chaudhary ◽

Shailesh T. Patel

Keyword(s):

Fixed Point ◽

Common Fixed Point ◽

Fixed Point Theorems ◽

Metric Spaces ◽

Complete Metric Space ◽

Contractive Condition ◽

Integral Type ◽

Complete Metric Spaces ◽

Common Fixed Point Theorems ◽

Common Fixed Point Theorem

In this paper, we prove some common fixed point theorems in complete metric spaces for self mapping satisfying a contractive condition of Integral type.

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On Asymmetric Distances

Analysis and Geometry in Metric Spaces ◽

10.2478/agms-2013-0004 ◽

2013 ◽

Vol 1 ◽

pp. 200-231 ◽

Cited By ~ 6

Author(s):

Andrea C.G. Mennucci

Keyword(s):

Total Variation ◽

Calculus Of Variations ◽

Distance Function ◽

Metric Space ◽

Metric Spaces ◽

Geodesic Segment ◽

Intrinsic Metric ◽

Typical Application ◽

Variation Formula

Abstract In this paper we discuss asymmetric length structures and asymmetric metric spaces. A length structure induces a (semi)distance function; by using the total variation formula, a (semi)distance function induces a length. In the first part we identify a topology in the set of paths that best describes when the above operations are idempotent. As a typical application, we consider the length of paths defined by a Finslerian functional in Calculus of Variations. In the second part we generalize the setting of General metric spaces of Busemann, and discuss the newly found aspects of the theory: we identify three interesting classes of paths, and compare them; we note that a geodesic segment (as defined by Busemann) is not necessarily continuous in our setting; hence we present three different notions of intrinsic metric space.

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