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In this paper, we introduced two new generalized metric spaces called partial b_{v}(s) and b_{v}({\theta}) metric spaces which extend b_{v}(s) metric space, b-metric space, rectangular metric space, v-generalized metric space, partial…
We give a characterization of completely regular topological spaces. Applying some recent results for supinf problems in completely regular topological spaces we establish a variational principle for saddle points. Well-posedness of saddle…
We classify the metric spaces that can be approximated by finite homogeneous ones.
In this paper, we introduce the notion of bicomplex partial b-metric space and prove some common fixed point theorems. Our results generalize and expand some of the literature's well known results. We also explore some of the applications…
Let Y be a locally convex Hausdorff space, K \subset E a cone and \leq_K the partial order defined by K. Let (X, p) be a TV S- cone metric space, {\phi} : K \rightarrow K a vectorial comparison function and f : X \rightarrow X such that…
In this paper a generalized topological central point theorem is proved for maps of a simplex to finite-dimensional metric spaces. Similar generalizations of the Tverberg theorem are considered.
We establish common fixed point theorems for two pairs of weakly compatible self-mappings using an auxiliary function of two variables. Unlike classical results, our theorems do not assume continuity of the mappings and require completeness…
In this paper, we introduce a new category of mappings within metric spaces, specifically focusing on three-point analogs of the well-established Chatterjea type mappings. We demonstrate that Chatterjea type mappings and their three-point…
We observe that the category of topological space, uniform spaces, and simplicial sets are all, in a natural way, full subcategories of the same larger category, namely the simplicial category of filters; this is, moreover, implicit in the…
We introduce the metric space valued in partially ordered groups, and define the convergence of sequences and the multi-valued weak contractions, etc., on the space. We then establish endpoint theorems for the defined maps. Our…
Some concepts, such as non-compactness measure and condensing operators, defined on metric spaces are extended to uniform spaces. Such extensions allow us to locate, in the context of uniform spaces, some classical results existing in…
We prove fixed point theorems in a space with a distance function that takes values in a partially ordered monoid. On the one hand, such an approach allows one to generalize some fixed point theorems in a broad class of spaces, including…
This paper gives some relating results for various concepts of convexity in metric spaces such as midpoint convexity, convex structure, uniform convexity and near-uniform convexity, Busemann curvature and its relation to convexity. Some…
We study the topology of metric spaces which are definable in o-minimal expansions of ordered fields. We show that a definable metric space either contains an infinite definable discrete set or is definably homeomorphic to a definable set…
Some examples of three-dimensional metrics of constant curvature defined by solutions of nonlinear integrable differential equations and their generalizations are constructed. The properties of Riemann extensions of the metrics of constant…
Persistent homology is a popular and useful tool for analysing finite metric spaces, revealing features that can be used to distinguish sets of unlabeled points and as input into machine learning pipelines. The famous stability theorem of…
Recently $S_{b}$-metric spaces have been introduced as the generalizations of metric and $S$-metric spaces. In this paper we investigate some basic properties of this new space. We generalize the classical Banach's contraction principle…
Three themes of general topology: quotient spaces; absolute retracts; and inverse limits - are reapproached here in the setting of metrizable uniform spaces, with an eye to applications in geometric and algebraic topology. The results…
In this paper, we propose a generalized notion of a distance function, called a $g$-metric. The $g$-metric with degree $n$ is a distance of $n+1$ points, generalizing the ordinary distance between two points and $G$-metric between three…
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…