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Assessment of rock mass quality significantly impacts the design and construction of underground and open-pit mines from the point of stability and economy. This study develops the novel Gromov-Hausdorff distance for rock quality (GHDQR) methodology for rock mass quality rating based on multi-criteria grey metric space. It usually presents the quality of surrounding rock by classes (metric spaces) with specified properties and adequate interval-grey numbers. Measuring the distance between surrounding rock sample characteristics and existing classes represents the core of this study. The Gromov-Hausdorff distance is an especially useful discriminant function, i.e. a classifier to calculate these distances, and assess the quality of the surrounding rock. The efficiency of the developed methodology is analyzed using the Mean Absolute Percentage Error (MAPE) technique. Seven existing methods, such as the Gaussian cloud method, Discriminant method, Mutation series method, Artificial neural network (ANN), Support vector machine (SVM), Grey wolf optimizer and Support vector classification method (GWO-SVC) and Rock mass rating method (RMR) are used for comparison with the proposed GHDQR method. The share of the highly accurate category of 85.71% clearly indicates compliance with actual values obtained by the compared methods. The results of comparisons showed that the model enables objective, efficient, and reliable assessment of rock mass quality. [ABSTRACT FROM AUTHOR]

We introduce a new type of mappings in metric spaces which are three-point analogue of the well-known Chatterjea type mappings, and call them generalized Chatterjea type mappings. It is shown that such mappings can be discontinuous as is the case of Chatterjea type mappings and this new class includes the class of Chatterjea type mappings. The fixed point theorem for generalized Chatterjea type mappings is proven. [ABSTRACT FROM AUTHOR]

In 2018, Erdal Karapinar introduced the concept of interpolative Kannan operators, a novel adaptation of the Kannan mapping originally defined in 1969 by Kannan. This new mapping condition is more lenient than the basic contraction condition. In this paper, we study the concept by introducing the IKC-iterated function/multi-function system using interpolative Kannan operators, including a broader area of mappings. Moreover, we establish the Collage Theorem endowed with the iterated function system (IFS) based on the IKC, and show the well-posedness of the IKC-IFS. Interpolative Kannan contractions are meaningful due to their applications in fractals, offering a more versatile framework for creating intricate geometric structures with potentially fewer constraints compared to classical approaches. [ABSTRACT FROM AUTHOR]

The aim of this paper is to introduce a new type of multi-valued operators and to present some basic problems of the fixed points and strict fixed points for them. Obtained results generalize, complement and extend classical results given by Ćirić (Mat. Vesnik 9 (24): 265-272, (1972)) or Nadler (Pacific J. Math. 30: 475-488 (1969)), as well as recent results given by Alecsa and PetruŞel (Anal. Univ. Vest Timisoara, LVII (1): 23-42 (2019)). [ABSTRACT FROM AUTHOR]

The Roe algebra C * (X) is a noncommutative C * -algebra reflecting metric properties of a space X, and it is interesting to understand the correlation between the Roe algebra of X and the (uniform) Roe algebra of its discretization. Here, we perform a minor step in this direction in the simplest non-trivial example, namely X = R , by constructing a continuous field of C * -algebras over [ 0 , 1 ] , with the fibers over non-zero points constituting the uniform C * -algebra of the integers, and the fibers over 0 constituting a C * -algebra related to R. [ABSTRACT FROM AUTHOR]

In the present study, we prove generalizations of Banach, Kannan, Chatterjea, Čirič-Reich-Rus fixed point theorems, as well as of the fixed point theorem for mapping contracting perimeters of triangles. We consider corresponding mappings in semimetric spaces with triangle functions introduced by Bessenyei and Pâles. Such an approach allows us to derive corollaries for various types of semimetric spaces such as metric spaces, ultrametric spaces, and b-metric spaces. The significance of these generalized theorems extends across multiple disciplines, such as optimization, mathematical modeling, and computer science. They may serve to establish stability conditions, demonstrate the existence of optimal solutions, and improve algorithm design. [ABSTRACT FROM AUTHOR]

This article is a revision and correction of the chapter book [S. Hadi Bonab, V. Parvaneh, Z. Bagheri, ηA-Admissible Mappings for Four Maps in C*-Algebra-Valued MP-Metric Spaces with an Application, In: P. Debnath, Delfim F. M. Torres, Yeol Je Cho, Advanced Mathematical Analysis and its Applications, CRC Press, 2023, 97-113.]. In this article, we first introduce the concept of η-admissible mapping in C* -algebra valued MP-metric spaces, which is a generalization and combination of ”modular metric spaces”, ”parametric metric spaces” and ”C* -algebra-valued metric spaces”. Then, for four mappings in these spaces, we prove several fixed-point theorems. We give an example and an application regarding the solvability of operator equations and integral equations, respectively, to support the new findings. [ABSTRACT FROM AUTHOR]

In this manuscript, utilizing interpolative contractions with fractional forms, some unique fixed-point results were studied in the context of extended b-metric spaces. For the validity of the presented results some examples are given. In the last section an existence theorem is provided to study the existence of a solution for the Fredholm integral equation. [ABSTRACT FROM AUTHOR]

Copyright of Misan Journal of Academic Studies is the property of Republic of Iraq Ministry of Higher Education & Scientific Research (MOHESR) and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

We introduce a weak Gurov–Reshetnyak class and discuss its connections to a weak Muckenhoupt A_\infty condition and a weak reverse Hölder inequality in the setting of metric measure spaces with a doubling measure. A John–Nirenberg type lemma is shown for the weak Gurov–Reshetnyak class which gives a specific decay estimate for the oscillation of a function. It implies that a function in the weak Gurov–Reshetnyak class satisfies the weak reverse Hölder inequality. This comes with an upper bound for the reverse Hölder exponent depending on the Gurov–Reshetnyak parameter which allows the study of the asymptotic behavior of the exponent. [ABSTRACT FROM AUTHOR]

In this work, we analyse the class of strictly pseudocontractive mappings in general metric spaces by providing a comprehensive and appropriate definition of a strictly pseudocontractive mapping, which serves as a natural extension of the existing notion. Moreover, we establish its various characterizations and explore several significant properties of these mappings in relation to fixed point theory in CAT(0) spaces. Specifically, we establish that these mappings are Lipschitz continuous, satisfying the demiclosedness-type property, and possessing a closed convex fixed point set. Furthermore, we show that the fixed points of the mappings can be effectively approximated using an iterative scheme for fixed points of nonexpansive mappings. The results in this work contribute to a deeper understanding of strictly pseudocontractive mappings and their applicability in the context of fixed point theory in metric spaces. [ABSTRACT FROM AUTHOR]

In this work, the set of all functions that are Fourier transformable with regard to their structure both algebraic and topological is taken into account. Certain topological properties of the set of Fourier transformable functions with the help of a metric are described. Also determines the proofs of the statements that the set of all Fourier transformable functions is a commutative semigroup with respect to the convolution operation as well as Abelian group with respect to the operation of addition. Metric for two functions belonging to the set of all Fourier transformable functions is defined and the proof that the Fourier transformable functions space is complete with our metric is given. The separability theorem and that the Fourier transformable functions space is disconnected are also discussed. [ABSTRACT FROM AUTHOR]

In this article, we present two resilient algorithms, the improved alternative hard c‐means (IAHCM) and the improved alternative fuzzy c‐means (IAFCM). We implement the Gaussian distance‐dependent function proposed by Zhang and Chen (D.‐Q. Zhang and Chen, 2004). In some cases, Zhang and Chen's metric distance does not account for the clustering centroid effect predicted by the large value. R* is employed in IAHCM and IAFCM to discover robust results while minimizing its sensitivity. Experiments are conducted using two‐and three‐dimensional data, including Diamond and Iris real‐world data. The results are based on demonstrating the robust simplicity and applicability of the offered algorithms. Similarly, computational complexity is assessed. [ABSTRACT FROM AUTHOR]

In this study, we prove the existence and uniqueness of a best proximity point in the setting of non-Archimedean modular metric spaces via the concept of simulation functions. A non-Archimedean metric modular is shaped as a parameterized family of classical metrics; therefore, for each value of the parameter, the positivity, the symmetry, the triangle inequality, or the continuity is ensured. Also, we demonstrate how analogous theorems in modular metric spaces may be used to generate the best proximity point results in triangular fuzzy metric spaces. The utility of our findings is further demonstrated by certain examples, illustrated consequences, and an application to fuzzy fractional differential equations. [ABSTRACT FROM AUTHOR]

The study deals with plastic and non-plastic sub-spaces A of the real-line E with the usual Euclidean metric d. It investigates non-expansive bijections, proves properties of such maps, and demonstrates their relevance by hands of examples. Finally, it is shown that the plasticity property of a sub-space A contains at least two complementary questions, a purely geometric and a topological one. Both contribute essential aspects to the plasticity property and get more critical in higher dimensions and more abstract metric spaces. [ABSTRACT FROM AUTHOR]

This paper is dedicated to the memory of the esteemed Serbian mathematician Slaviša B. Prešić (1933–2008). The primary aim of this survey paper is to compile articles on Prešić-type mappings published since 1965. Additionally, it introduces a novel class of symmetric contractions known as Prešić–Menger and Prešić–Ćirić–Menger contractions, thereby enriching the literature on Prešić-type mappings. The paper endeavors to furnish young researchers with a comprehensive resource in functional and nonlinear analysis. The relevance of Prešić's method, which generalizes Banach's theorem from 1922, remains significant in metric fixed point theory, as evidenced by recent publications. The overview article addresses the growing importance of Prešić's approach, coupled with new ideas, reflecting the ongoing advancements in the field. Additionally, the paper establishes the existence and uniqueness of fixed points in Menger spaces, contributing to the filling of gaps in the existing literature on Prešić's works while providing valuable insights into this specialized domain. [ABSTRACT FROM AUTHOR]

The analogue of polar coordinates in the Euclidean space, a polar decomposition in a metric space, if well-defined, can be very useful in dealing with integrals with respect to a sufficiently regular measure. In this note we handle the technical details associated with such polar decompositions. Supplementary Information: The online version contains the Armenian language version of the article available at https://doi.org/10.1007/s10958-023-06674-w. [ABSTRACT FROM AUTHOR]

Let (X, d) be a metric space, f: X → X be a mapping and G(., f(.)) be an admissible perturbation of f. In this paper we study the following problems: In which conditions imposed on f and G we have the following: (DDE) data dependence estimate for the mapping f perturbation; (UH) Ulam-Hyers stability for the equation, x = f(x); (WP) well-posedness of the fixed point problem for f; (OP) Ostrowski property of the mapping f. Some research directions are suggested. [ABSTRACT FROM AUTHOR]

In this paper, a general idea of Presic type L-fuzzy fixed point results using some weakly contractive conditions in the setting of metric space is initiated. Stability of L-fuzzy mappings and associated new concepts are proposed herein to complement their corresponding notions related to crisp multi-valued and single-valued mappings. Illustrative nontrivial examples are provided to support the assertions of our main results. [ABSTRACT FROM AUTHOR]

This thesis consists of four parts. In the first chapter, the basic definitions and theorems that will be used throughout the thesis are given. In the second part, we obtain some of the best periodic proximity point results in metric spaces for p-contraction type mappings. Thus, we generalize and improve the similar results existing in the literature. In the third section, we demonstrate some of the best periodic proximity point results in metric spaces for nonunique contraction mappings. Some generalizations of both the fixed point and best proximity point results have been obtained for nonunique contraction mappings. [ABSTRACT FROM AUTHOR]

The process of sorting or categorizing objects or information about these objects into clusters according to certain criteria is a fundamental procedure in data analysis. Where it is feasible to determine the distance metric for any pair of objects, the significance and reliability of the separation can be evaluated by calculating the separation/segregation power (SP) index proposed herein. The latter index is the ratio of the average inter distance to the average intra distance, independent of the scale parameter. Here, the calculated SP value is compared to its statistical distribution obtained by a simulation study for a given partition under the homogeneity null hypothesis to draw a conclusion using standard statistical procedures. The proposed concept is illustrated using three examples representing different types of objects under study. Some general considerations are given regarding the nature of the SP distribution under the null hypothesis and its dependence on the number of divisions and the amount of data within them. A detailed modus operandi (working method) for analyzing a metric data partition is also offered. [ABSTRACT FROM AUTHOR]

In this paper, the concepts of Wardowski-type set-valued contractions and Işik-type set-valued contractions are introduced and fixed point theorems for such contractions are established. A positive answer to the open Question is given. Examples to support main theorems and an application to integral inclusion are given. [ABSTRACT FROM AUTHOR]

In our recent research we studied a feasibility problem with infinitely many sets in a metric space, presented a novel algorithm and analyzed its convergence. In the present paper we study our algorithm introduced in that recent work for common fixed problem taking into account computational errors. We show that our algorithm generates a good approximate solution, if computational errors are bounded from above by a small positive constant. [ABSTRACT FROM AUTHOR]

In this paper, we introduce a pseudometric on the family of isometry classes of (extended) metric spaces. Using it, we obtain a natural compactification of the Gromov–Hausdorff space, which is compatible with ultralimit. [ABSTRACT FROM AUTHOR]

In an outstanding article published in 2008, Suzuki obtained a nice generalization of the Banach contraction principle, from which a characterization of metric completeness was derived. Although Suzuki's theorem has been successfully generalized and extended in several directions and contexts, we here show by means of a simple example that the problem of achieving, in an obvious way, its full extension to the framework of w-distances does not have an emphatic response. Motivated by this fact, we introduce the concept of presymmetric w-distance on metric spaces. We also give some properties and examples of this new structure and show that it provides a reasonable setting to obtain a real and hardly forced w-distance generalization of Suzuki's theorem. This is realized in our main result, which consists of a fixed point theorem that involves presymmetric w-distances and certain contractions of Suzuki-type. We also discuss the relationship between our main result and the well-known w-distance full generalization of the Banach contraction principle, due to Suzuki and Takahashi. Connected to this approach, we prove another fixed point result that compares with our main result through some examples. Finally, we state a characterization of metric completeness by using our fixed point results. [ABSTRACT FROM AUTHOR]

In the context of a complete metric space, the most important fixed-point result for multi-valued operators was given in 1969. Many extensions of this fixed-point principle for multi-valued operators were proved by different authors. Based on some of the above-mentioned results, we introduce the notion of the multi-valued Feng–Liu-type operator and we construct an abstract fixed-point theory for this general class of multi-valued operators. Our results extend and complement some theorems in metric fixed-point theory for multi-valued operators. An application to a Cauchy problem related to a first-order differential inclusion is also given. In this case, our theorem improves several previous theorems on this subject by relaxing the contraction-type condition (with respect to its second argument) on the multi-valued right-hand side. [ABSTRACT FROM AUTHOR]

In this study, we explored a novel type of contraction, known as paired contraction (PC), to establish fixed points in metric spaces. It has been demonstrated that mappings possessing the PC property are continuous. We have also provided proofs for the existence of fixed points for such mappings with the classical Banach fixed point theorem emerging as a corollary. Furthermore, we presented examples of mappings that do not satisfy the standard contraction condition, but do exhibit the PC property. [ABSTRACT FROM AUTHOR]

We show that limsup sets generated by a sequence of open sets in compact Ahlfors s-regular (0 < s < ∞) space (X , 풝 , μ , ρ) belong to the classes of sets with large intersections with index λ, denoted by G λ (X) , under some conditions. In particular, this provides a lower bound on Hausdorff dimension of such sets. These results are applied to obtain that limsup random fractals with indices γ2 and δ belong to G s − δ − γ 2 (X) almost surely, and random covering sets with exponentially mixing property belong to G s 0 (X) almost surely, where s0 equals to the corresponding Hausdorff dimension of covering sets almost surely. We also investigate the large intersection property of limsup sets generated by rectangles in metric space. [ABSTRACT FROM AUTHOR]

Copyright of Duzce University Journal of Science & Technology is the property of Duzce University Journal of Science & Technology and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

Outlier detection is an important data mining technique. In this article, the triangle inequality of distances is leveraged to design a pre-cutoff value (PCV) algorithm that calculates the outlier degree pre-threshold without additional distance computations. This algorithm is suitable for accelerating various metric space outlier detection algorithms. Experimental results on multiple real datasets demonstrate that the PCV algorithm reduces the runtime and number of distance computations for the iORCA algorithm by 14.59% and 15.73%, respectively. Even compared to the new high-performance algorithm ADPOD, the PCV algorithm achieves 1.41% and 0.45% reductions. Notably, the non-outlier exclusion for the first data block in the dataset is significantly improved, with an exclusion rate of up to 36.5%, leading to a 23.54% reduction in detection time for that data block. While demonstrating excellent results, the PCV algorithm maintains the data type generality of metric space algorithms. [ABSTRACT FROM AUTHOR]

G. Klir proposed to describe the behavior of complex systems using behavior functions (BFs) - invariant constraints on the set of system states. BFs are one of the most productive tools for studying the functioning of systems. To study systems, it is necessary to have a metric for measuring of the difference between two BFs. To describe BFs modern researchers do not use distributions other than probability or possibility. But these distributions can be considered as special cases of Sugeno fuzzy measures, the use of which greatly expands the possibilities in the study of systems. However, metrics to measure the difference between fuzzy measures have not been developed. Therefore, in this article, the authors proposed a new metric and an algorithm for its calculation for the case when BFs are described by Sugeno fuzzy measures. This metric is based on the Cartesian product of fuzzy measures and the use of our proposed concentration function. The metric makes it possible to compare the behavior of systems in the case of describing BFs by Sugeno fuzzy measures with different modalities, as well as to ensure the priority of taking into account the set of the most significant states of the system. [ABSTRACT FROM AUTHOR]

This paper presents some existence and uniqueness results for a solution of a system of equations. Our results extend and generalize the well-known and celebrated results of Boyd and Wong [Proc. Amer. Math. Soc. 20 (1969)], Matkowski [Dissertations Math. (Rozprawy Mat.) 127 (1975)], Proinov [Nonlinear Anal. 64 (2006)], Ri [Indag. Math. (N. S.) 27 (2016)] and many others. We also present some illustrative examples to validate our results. [ABSTRACT FROM AUTHOR]

Recently, Karapinar introduced a new Hardy-Rogers type contractive mapping using the concept of interpolation and proved a fixed point theorem in complete metric space. This new type of mapping, called "interpolative Hardy-Rogers type contractive mapping" is a generalization of Hardy-Rogers's fixed point theorem. Following this direction of research, in this paper, we will present some fixed point results of Hardy-Rogers-type for cyclic mappings on complete metric spaces. Moreover, an example is given to illustrate the usability of the obtained results. [ABSTRACT FROM AUTHOR]

This paper continues a series discussing flaws in published assertions concerning fixed points in digital images. [ABSTRACT FROM AUTHOR]

In this article, we introduce the fundamentals of the theory of demicontractive mappings in metric spaces and expose the key concepts and tools for building a constructive approach to approximating the fixed points of demicontractive mappings in this setting. By using an appropriate geodesic averaged perturbation technique, we obtained strong convergence and Δ-convergence theorems for a Krasnoselskij-Mann type iterative algorithm to approximate the fixed points of quasinonexpansive mappings within the framework of CAT(0) spaces. The main results obtained in this nonlinear setting are natural extensions of the classical results from linear settings (Hilbert and Banach spaces) for both quasi-nonexpansive mappings and demicontractive mappings. We applied our results to solving an equilibrium problem in CAT(0) spaces and showed how we can approximate the equilibrium points by using our fixed point results. In this context we also provided a numerical example in the case of a demicontractive mapping that is not a quasi-nonexpansive mapping and highlighted the convergence pattern of the algorithm in Table 1. It is important to note that the numerical example is set in non-Hilbert CAT(0) spaces. [ABSTRACT FROM AUTHOR]

The present paper is on fixed point theory in set valued analysis. Here putting several concepts together, we define a set valued contraction and establish that such contractions have fixed points in a complete metric space. We have two main theorems in one of which we use α -regularity condition of the space as a substitute of the continuity requirement on the multivalued contraction. There are some illustrative examples and corollaries. We also perform stability analysis of fixed point sets. We establish that the fixed point sets associated with the mappings we consider in our theorems are stable. In the last section we discuss some consequences of the main results of this paper. [ABSTRACT FROM AUTHOR]

In this paper, we use an inequality involving a coupled multivalued mapping and a singlevalued mapping to obtain a coupled coincidence point theorem. We discuss special conditions under which coupled common fixed point theorems are obtained. The result combines several ideas prevalent in fixed point theory studies. There are several corollaries and illustrative examples. The Hausdorff-Pompeiu metric between sets is used. The work is in the context of metric spaces and is a part of set-valued analysis with the singlevalued consequences. [ABSTRACT FROM AUTHOR]

This article introduces the novel concept of an extended parametric S b -metric space, which is a generalization of both S b -metric spaces and parametric S b -metric spaces. Within this extended framework, we first establish an analog version of the Banach fixed-point theorem for self-maps. We then prove an improved version of the Banach contraction principle for symmetric extended parametric S b -metric spaces, using an auxiliary function to establish the desired result. Finally, we provide illustrative examples and an application for determining solutions to Fredholm integral equations, demonstrating the practical implications of our work. [ABSTRACT FROM AUTHOR]

Approximate nearest neighbor search (ANNS) for high dimensional data has received extensive research efforts. Many existing ANNS methods in metric spaces are essentially based on the permutation of pivots, or pre-selected reference points, which are ordered by their distances to the data. Unfortunately, most of these permutation-based methods are quite memory demanding, because of either complexity of index structure, excessive pivots, or insufficient exploitation of distances. This paper proposes the reduced permutation array (RPA), a delicate integration of existing technical elements based on in-depth understanding, for recall@R ANNS in metric spaces. As an array, for each data element, RPA stores only l identities (IDs) of its nearest pivots out of k pre-selected ones (l « k). During search, the order of distances from each data element to the query is approximated by a score function based on the distances from its nearest pivots to the query, and a bounded heap is maintained to store R candidate results. RPA is simple, memory-efficient, and scalable. Experiments show that RPA is approximately 3 times more memory-efficient than existing methods on average. The research results can provide an effective ANNS method for massive data in a single-machine environment with limited memory resources. [ABSTRACT FROM AUTHOR]

We obtain precise estimates, in terms of the measure of balls, for the Besov capacity of annuli and singletons in complete metric spaces. The spaces are only assumed to be uniformly perfect with respect to the centre of the annuli and equipped with a doubling measure. [ABSTRACT FROM AUTHOR]

The continuous production of heterogeneous internet of things (IoT) data created a new challenge, which is their storage and retrieve efficiently. In this work, a new method of indexing, called threshold distance (TD), is proposed in the fog‐cloud architecture. In this method, the fog layer is divided into two levels: a clustering level and an indexing level. In the clustering fog level, the first data flow is grouped into clusters of homogenous objects using the density‐based spatial clustering applications with noise (DBSCAN) algorithm. In the indexing fog level, objects in each cluster are indexed in separated generalized hyperplane‐trees (GHT). After the clustering of the next data flow, objects are inserted in existing GHT or new GHT are created according the comparison of the distances between centers of the next clusters and those of the first clusters (took as representatives of their corresponding indexes) with a threshold distance value. To test the efficiency of the TD method, the experimental results were compared with those of our second proposed method called creation of a new tree (CNT) in which, data of each cluster is indexed in a new GHT. The experimental results show that the efficiency of the TD method in GHT construction depend on the size of the data flow. For the parallel kNN search, the TD method proved its efficiency whatever the size of the data flow. [ABSTRACT FROM AUTHOR]

The purpose of this study is to present fixed-point results for Suzuki-type multi-valued maps using relation theory. We examine a range of implications that arise from our primary discovery. Furthermore, we present two substantial cases that illustrate the importance of our main theorem. In addition, we examine the stability of fixed-point sets for multi-valued maps and the concept of well-posedness. We present an application to a specific functional equation which arises in dynamic programming. [ABSTRACT FROM AUTHOR]

In this work we show that if iterates of a nonexpansive self-mapping of a complete metric with a graph converge uniformly on a subset of the space, then this convergence is stable under the presence of small computational errors. [ABSTRACT FROM AUTHOR]

We initiate the study of fine p-(super)minimizers, associated with p-harmonic functions, on finely open sets in metric spaces, where 1 < p < ∞ . After having developed their basic theory, we obtain the p-fine continuity of the solution of the Dirichlet problem on a finely open set with continuous Sobolev boundary values, as a by-product of similar pointwise results. These results are new also on unweighted Rn. We build this theory in a complete metric space equipped with a doubling measure supporting a p-Poincaré inequality. [ABSTRACT FROM AUTHOR]

Our aim in this article is to show that all metric fixed point theorems hold for quasi-metric spaces (X, δ) (without symmetry). In fact, we show some well-known theorems on metric spaces hold for quasi-metric spaces from the beginning. We check this fact for the Banach contraction principle, the Covitz-Nadler fixed point theorem, the Rus-Hicks-Rhoades fixed point theorem, and others. In these theorems the concepts of continuity and completeness can be replaced by orbital continuity and T-orbital completeness for a selfmap T, respectively. Consequently, we improve and generalize the basic known theorems in the metric fixed point theory. [ABSTRACT FROM AUTHOR]

What is the analogous notion of Gromov–Hausdorff convergence for sequences of spacetimes? Since a Lorentzian manifold is not inherently a metric space, one cannot simply use the traditional definition. One approach offered by Sormani and Vega (Class Quant Gravity, 33:085001, 2016) is to define a metric space structure on a spacetime by means of the null distance. Then one can define convergence of spacetimes using the usual definition of Gromov–Hausdorff convergence. In this paper we explore this approach by giving many examples of sequences of warped product spacetimes with the null distance converging in the Gromov–Hausdorff sense. In addition, we give an optimal convergence theorem which shows that under natural geometric hypotheses a sequence of warped product spacetimes converge to a specific limiting warped product spacetime. The examples given further serve to show that the hypotheses of this convergence theorem are optimal. [ABSTRACT FROM AUTHOR]

We establish a stability theorem for geometric separating flows on metric spaces, which may or may not be compact. Notably, this result extends Thomas' stability theorem (Proc London Math Soc. 45:479–505 1982). To prove our theorem, we employ set-valued analysis (Aubin and Frankowska, 1990). We give some applications of our result. [ABSTRACT FROM AUTHOR]

We examine the role of the convex structure in a metric space on which it is defined. First, we introduce the notion of extreme point and face of a convex set. Second, we present the idea of core in a convex metric space. Several properties are proved and examples to support are given. [ABSTRACT FROM AUTHOR]

In the characterization of the space debris environment, the computation of the orbit of the debris objects is usually conducted by considering the association of short sequences of observations called tracklets. In case the orbits can be already determined with sufficient accuracy from single tracklets, it is necessary to define a criterion to decide if two calculated orbits correspond to the same object. One possibility is to introduce a definition of distance between orbits and to consider a threshold below which the two orbits are considered to be originating from the same object. The concept of distance is quite general and leaves room to different definitions. There are different ways to describe and to parameterize the space of the possible orbits. In this article, new metrics are proposed which extend distance definitions suggested in previous works. In these metrics in addition to orbital plane and orbital shape, also the position of the object along the orbit is taken into account. The obtained distances are scaled according to the orbit covariance. This has the advantage that the distance between orbits with different accuracy can be evaluated. The proposed metrics are then compared with existing common metrics to assess their applicability. [ABSTRACT FROM AUTHOR]

Fixed-figure problem has been introduced as a generalization of fixed circle problem and investigated a geometric generalization of fixed point theory. In this sense, we prove new fixed-figure results with some illustrative examples on metric spaces. For this purpose, we use KMK-type contractions, that is, Kannan type and Meir-Keeler type contractions. [ABSTRACT FROM AUTHOR]