scholarly journals Some New Results in Partial Cone $b$-Metric Space

2020 ◽  
pp. 67-73
Author(s):  
Zeynep KALKAN ◽  
Aynur ŞAHİN
Keyword(s):  
Metric Space ◽  
Partial Cone

Fixed point theorem for quasi-contractive mapping in partial cone metric space

2014 ◽  
Vol 26 (5-6) ◽  
pp. 1153-1159 ◽  
Author(s):  
Wajdi Chaker ◽  
Abdelaziz Ghribi ◽  
Aref Jeribi ◽  
Bilel Krichen
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Point Theorem ◽  
Metric Space ◽  
Contractive Mapping ◽  
Cone Metric Space ◽  
Partial Cone ◽  
Cone Metric

scholarly journals The asymptotically regularity and sequences in partial cone b-metric spaces with application

Filomat ◽  
2016 ◽  
Vol 30 (10) ◽  
pp. 2749-2760 ◽  
Author(s):  
Jerolina Fernandez ◽  
Neeraj Malviya ◽  
Brian Fisher
Keyword(s):  
Fixed Point ◽  
Metric Space ◽  
Fixed Point Theorems ◽  
Metric Spaces ◽  
Partial Metric ◽  
Regular Maps ◽  
Partial Cone ◽  
Partial Metric Spaces ◽  
New Space ◽  
Asymptotically Regular

The aim of this paper is to propose a new space called partial cone b-metric space by using both the notions of cone b-metric spaces and partial metric spaces and by defining asymptotically regular maps and sequences. We also prove some fixed point theorems for such maps and sequences. Our results extend and generalize some interesting results of [11] and [21] in partial cone b-metric space. An example is also given to support the validity of our results.

On Asymmetric Distances

2013 ◽  
Vol 1 ◽  
pp. 200-231 ◽  
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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