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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.

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.

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]

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]

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]

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]

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]

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]

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 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]

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]

The study deals with plastic and non-plastic sub-spaces A of the real-line ℝ 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.

Recent studies have highlighted fixed point theorems in the context of bicomplex valued metric spaces, utilizing rational type contractions with coefficients defined by two-variable control functions. In our research, we extend these findings by proposing new theorems for identifying common fixed points within bicomplex valued metric spaces, employing rational type contractions characterized by three-variable control functions as coefficients. We have refined the contraction conditions presented in numerous existing theorems by substituting constants with a limited number of control functions for more versatility in bicomplex valued metric spaces. This advancement broadens the scope of several significant findings in the literature. To demonstrate the efficacy of our results, we offer compelling examples that validate our theorems. Furthermore, we apply our primary findings to effectively address the Urysohn integral equation system, showcasing the practical application of our research.

In this work, a new class of general contractive mappings, with the name Jaggi-Suzuki-type hybrid (K-α-ϕ)-contractive mapping is discussed in metric space equipped with a graph and new criteria for which the mapping is a Picard operator are studied. The superiority of this type of contractive mapping lies in the fact that its contractive inequality can be fixed in different ways, depending on the specified constants. Substantial illustrations are furnished to validate the axioms of our obtained ideas and to show their difference from the existing concepts. Supplementarily, some corollaries which collapse our obtained notion to recently propounded results in the literature are brought out and analysed.

The well-known Caristi fixed point theorem has numerous generalizations and modifications. Recently there have appeared its equivalent dual forms and generalizations based on new concept of lower semicontinuity from above by several authors. In the present article, we give new proofs of such new versions and their equivalent formulations by applying our Metatheorem in the ordered fixed point theory.

Let (X,d) be a quasi-metric space. A Rus-Hicks-Rhoades (RHR) map f:X→X is the one satisfying d(fx,f2x)≤αd(x,fx) for every x∈X, where α∈[0,1). In our previous work [37], we collected various fixed-point theorems closely related to RHR maps. In the present article, we collect almost all the things we know about RHR maps and their examples. Moreover, we derive new classes of generalized RHR maps and fixed point theorems on them. Consequently, many of the known results in metric fixed point theory are improved and reproved in an easy way.

Any two points are close together in a

In order to study Maia type fixed point results for several well-known contractions, we suggest two novel contractions called $ \mathcal{A} $-contraction and $ \mathcal{A}' $-contraction. The majority of the Maia type fixed point results for various contractions can now be unified through these, which eliminate the need to manage various contractions individually. The advantage of including such contractions in the study of Maia type fixed point results has been demonstrated in suitable examples. We present an application of one of our established results towards the conclusion of the paper.

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.

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.

This paper deals with the existence and uniqueness of common fixed points in metric and dislocated metric spaces. In addition, an application and some illustrative examples are given in order to justify the validity and credibility of our results, also, their superiority over some similar theorems existing in unique common fixed points theory’s domain.

Topology is branch of modern mathematics that plays an important role in applications of biology. The aim of this paper is to study DNA sequence mutations using multisets, relations, metric functions, topology and association indices. Moreover, we use association indices to study the similarity between DNA sequences. These different ways of identifying a mutation help biologists to make a decision. A decision of mutation that depends on metrics between two sequences of genes and the topological structure produced by their relationship is presented.

In this paper, we obtain a generalization of a fixed point theorem given by Popescu [O. Popescu, Comput. Math. Appl., vol. 62, no. 10, pp. 3912-3919, 2011]. An example is also given to support our main result. [ABSTRACT FROM AUTHOR]

In 2007, in our joint work with D. Butnariu and S. Reich, we proved that if for a self-mapping of a complete metric that is uniformly continuous on bounded sets all its iterates converge uniformly on bounded sets, then this convergence is stable under the presence of small errors. In the present paper, we obtain an extension of this result for self-mappings of a metric space with a graph. [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]

In order to study Maia type fixed point results for several well-known contractions, we suggest two novel contractions called A-contraction and A'-contraction. The majority of the Maia type fixed point results for various contractions can now be unified through these, which eliminate the need to manage various contractions individually. The advantage of including such contractions in the study of Maia type fixed point results has been demonstrated in suitable examples. We present an application of one of our established results towards the conclusion of the paper. [ABSTRACT FROM AUTHOR]

Any two points are close together in a  -contraction by a factor of  . The function  Δ  is implied to be a contraction under this condition, but with a tighter bound on the contraction factor. In this paper, we introduce the notions of orthogonal  -contraction and orthogonal  α − -contraction and prove several fixed point results by utilizing these contraction mappings in the context of orthogonal metric spaces. Further, we provide several non-trivial examples to show the validity of our results. [ABSTRACT FROM AUTHOR]

We consider a new type of mappings in metric spaces which can be characterized as mappings contracting perimeters of triangles. It is shown that such mappings are continuous. The fixed point theorem for such mappings is proved and the classical Banach fixed-point theorem is obtained like a simple corollary. Examples of mappings contracting perimeters of triangles which are not contraction mappings are constructed. [ABSTRACT FROM AUTHOR]

This paper gives verifiable conditions for the existence of solutions of some set quasi-optimization problems involving Minkowski difference, where the objective maps are defined in complete metric spaces. Our proof method is not based on any scalarizing approach, and our existence results are written in terms of the given data of the problems. Several examples are provided. As applications of the main results of this paper, new results on the existence of robust solutions for uncertain multi-objective quasi-optimization problems with set-valued maps are formulated. [ABSTRACT FROM AUTHOR]

One of the tools for building new fixed-point results is the use of symmetry in the distance functions. The symmetric property of metrics is particularly useful in constructing contractive inequalities for analyzing different models of practical consequences. A lot of important invariant point results of crisp mappings have been improved by using the symmetry of metrics. However, more than a handful of fixed-point theorems in symmetric spaces are yet to be investigated in fuzzy versions. In accordance with the aforementioned orientation, the idea of Presic-type intuitionistic fuzzy stationary point results is introduced in this study within a space endowed with a symmetrical structure. The stability of intuitionistic fuzzy fixed-point problems and the associated new concepts are proposed herein to complement their corresponding concepts related to multi-valued and single-valued mappings. In the instance where the intuitionistic fuzzy-set-valued map is reduced to its crisp counterparts, our results complement and generalize a few well-known fixed-point theorems with symmetric structure, including the main results of Banach, Ciric, Presic, Rhoades, and some others in the comparable literature. A significant number of consequences of our results in the set-up of fuzzy-set- and crisp-set-valued as well as point-to-point-valued mappings are emphasized and discussed. One of our findings is utilized to assess situations from the perspective of an application for the existence of solutions to non-convex fractional differential inclusions involving Caputo fractional derivatives with nonlocal boundary conditions. Some nontrivial examples are constructed to support the assertions and usability of our main ideas. [ABSTRACT FROM AUTHOR]

Topology is branch of modern mathematics that plays an important role in applications of biology. The aim of this paper is to study DNA sequence mutations using multisets, relations, metric functions, topology and association indices. Moreover, we use association indices to study the similarity between DNA sequences. These different ways of identifying a mutation help biologists to make a decision. A decision of mutation that depends on metrics between two sequences of genes and the topological structure produced by their relationship is presented. [ABSTRACT FROM AUTHOR]

In this paper, we introduce four new types of contractions called in this order Kannan-type cyclic contraction via interpolation, interpolative Ćirić-Reich-Rus type cyclic contraction, and we prove the existence and uniqueness for a fixed point for each situation. [ABSTRACT FROM AUTHOR]

This paper continues a series discussing aws in published assertions concerning fixed points in digital metric spaces. [ABSTRACT FROM AUTHOR]

In this the research work deals mainly with fixed point theorems and their applications. The fuzzy topological spaces and quasi fuzzy metric spaces are introduced. Also, the variational principle and Christi's fixed point theorem in fuzzy topological spaces are established, the results of which are utilized to obtain a fixed point theorem for Manger probabilistic metric space. The compatible pair of reciprocally continuous mappings is defined and a fixed point theorem in a fuzzy metric space is obtained which generates a fixed point but does not force the map to be continuous. Further, V|/-compatible mapping is introduced in a fuzzy metric space and established the altering distances between the points using certain control functions which differ from the previous works. R-weakly commuting of type (A„) and non compatible mappings in fuzzy metric space are introduced which leads to the proof of fixed point theorem without assuming completeness of the space or continuity. [ABSTRACT FROM AUTHOR]

In this paper, we prove the existence and the uniqueness of a fixed point for pairs of self-mappings on (3, 2)-W-symmetrizable spaces using self-mappings similar to TF contractions in ordinary metric spaces, and we obtain two corollaries. [ABSTRACT FROM AUTHOR]

Let (C;D) be a nonempty pair of disjoint subsets of a metric space. Main purpose of this paper is to present a range of a convergence sequence to u 2 C [D such that d(Tu, fu) = dist(C, D), for mappings T, f: C [D &#8594, C [D. In fact, we give a generalization of best proximity point results for cyclic contractive mappings. To this end, we consider an example is presented to support the main result. [ABSTRACT FROM AUTHOR]

In recent years, J. R. Kider and Z.A. Hussain have introduced the notion of standard fuzzy metric space and some basic properties were proved. In this paper, we generalize this notion to the setting of single valued neutrosophic sets. Furthermore, some interesting properties related to this notion are studied such as the continuity property of the mappings defined on standard single valued neutrosophic metric spaces. As an application, we establish the Edelstein fixed point theorem for standard single valued neutrosophic metric spaces. [ABSTRACT FROM AUTHOR]