Pre-Symmetric w-Cone Distances and Characterization of TVS-Cone Metric Completeness

被引：0
|
作者：
Karimizad, Seyedeh Sara [1 ]
Rad, Ghasem Soleimani [2 ]
机构：
[1] Ilam Univ, Fac Basic Sci, Dept Math, POB 69315-516, Ilam, Iran
[2] Islamic Azad Univ, Young Researchers & Elite Club, POB 14778-93855, Tehran, Iran
来源：
MATHEMATICS | 2024年 / 12卷 / 12期
关键词：
pre-symmetric w-cone distance; TVS-CMS; Suzuki-type contraction; Minkowski functional; completeness; GENERALIZED C-DISTANCE; POINT THEOREMS; FIXED-POINTS; SPACES; PRINCIPLE; MAPPINGS; RESPECT;
D O I：
10.3390/math12121833
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
Motivated by two definitions of distance, "pre-symmetric w-distance" and "w-cone distance", we define the concept of a pre-symmetric w-cone distance in a TVS-CMS and introduce its properties and examples. Also, we discuss the TVS-cone version of the recent results obtained by Romaguera and Tirado. Meanwhile, using Minkowski functionals, we show the equivalency between some consequences concerning a pre-symmetric w-distance in a usual metric space and a pre-symmetric w-cone distance in a TVS-CMS. Then, some types of various w-cone-contractions and the relations among them are investigated. Finally, as an application, a characterization of the completeness of TVS-cone metric regarding pre-symmetric concept is performed, which differentiates our results from former characterizations.
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页数：10
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