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19 pages, 292 KB

Open AccessFeature PaperEditor’s ChoiceArticle

Fixed-Point Results and the Ekeland Variational Principle in Vector B-Metric Spaces

by Radu Precup and Andrei Stan

Axioms 2025, 14(4), 250; https://doi.org/10.3390/axioms14040250 - 26 Mar 2025

Cited by 1 | Viewed by 1220

In this paper, we extend the concept of b-metric spaces to the vectorial case, where the distance is vector-valued, and the constant in the triangle inequality axiom is replaced by a matrix. For such spaces, we establish results analogous to those in the b-metric setting: fixed-point theorems, stability results, and a variant of Ekeland’s variational principle. As a consequence, we also derive a variant of Caristi’s fixed-point theorem. Full article

(This article belongs to the Special Issue Fixed-Point Theory and Its Related Topics, 5th Edition)

18 pages, 315 KB

Open AccessArticle

Generalizations and Properties of Normalized Similarity Measures for Boolean Models

by Amelia Bădică, Costin Bădică, Doina Logofătu and Ionuţ-Dragoş Neremzoiu

Mathematics 2025, 13(3), 384; https://doi.org/10.3390/math13030384 - 24 Jan 2025

Cited by 1 | Viewed by 1670

Abstract

In this paper, we provide a closer look at some of the most popular normalized similarity/distance measures for Boolean models. This work includes the generalization of three classes of measures described as generalized Kulczynski, generalized Jaccard, and generalized Consonni and Todeschini measures, theoretical ordering of the similarity measures inside each class, as well as between classes, and positive and negative results regarding the metric properties of measures related to satisfying or not satisfying the triangle inequality axiom. Full article

(This article belongs to the Special Issue Mathematics and Applications)

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17 pages, 987 KB

Open AccessArticle

(L,M)-Fuzzy k-Pseudo Metric Space

by Yu Zhong, Xin Wu, Alexander Šostak and Fu-Gui Shi

Mathematics 2022, 10(7), 1151; https://doi.org/10.3390/math10071151 - 2 Apr 2022

Cited by 5 | Viewed by 2679

Abstract

Recently, the notion of a classical k-metric, which make the triangle inequality to a more general axiom:

d (x, z) \leq k (d (x, y) + d (y, z))

, has [...] Read more.

Recently, the notion of a classical k-metric, which make the triangle inequality to a more general axiom:

d (x, z) \leq k (d (x, y) + d (y, z))

, has been presented and is applied in many fields. In this paper, the definitions of an

(L, M)

-fuzzy k-pseudo metric and an

(L, M)

-fuzzy k-remote neighborhood ball system are introduced. It is proved that the category of

(L, M)

-fuzzy k-pseudo metric spaces is isomorphic to the category of

(L, M)

-fuzzy k-remote neighborhood ball spaces. Besides,

(L, M)

-fuzzy topological structures induced by an

(L, M)

-fuzzy k-pseudo metric are presented and their properties are investigated. Finally, the concept of a nest of pointwise k-pseudo metrics is proposed and it is shown that there is a one-to-one correspondence between

(L, M)

-fuzzy k-pseudo metrics and nests of pointwise k-pseudo metrics. Full article

(This article belongs to the Special Issue Fuzzy Convex Structures and Some Related Topics)

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