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Very recently, P. Saha et al. [A global optimality result in probabilistic spaces using control function. Optimization. 2021;70:2387–2400] studied the existence of best proximity points for Banach type ϕ-proximal contractions in the framework of Menger probabilistic metric spaces. In this paper, we present a simple proof of their main existence result which is based on a fixed point theorem for ϕ-contractive self-mappings in complete Menger PM-spaces due to B.S. Choudhury and K. Das [A new contraction principle in Menger spaces. Acta Math Sin. 2008;24:13791386]. [ABSTRACT FROM AUTHOR]

In 2020, Olia et al. [Olia, Z. E. D. D., Gordji, M. E. and Bagha, D. E. (2020). Banach fixed point theorem on orthogonal cone metric spaces. FACTA Universitatis (NIS) Ser. Math. Inform, 35, 1239-1250] examined orthogonal cone metric spaces. They assumed that P is a normal cone with normal constant K and that self mapping T is orthogonal continuous on the orthogonal cone metric space X in their study. This study now presentes certain required definitions on orthogonal cone metric spaces that were not previously given in [9]. The examples that show the link between existing and new definitions have also been included. The results are also generalized by eliminating the normalcy condition and utilizing point orthogonal continuity instead of general orthogonal continuity in the major results of [9]. The fundamental finding of the study is then generalized by removing the requirement of orthogonal continuity and introducing normality. In addition, certain outcomes of stated theorems are proven, and some examples are provided to demonstrate these theorems. [ABSTRACT FROM AUTHOR]

In a recent paper [I. Altun and A. Tasdemir, On best proximity points of interpolative proximal contractions, Quaestiones Math. (2020), DOI: ] the authors proved two best proximity point theorems for a new class of non-self mappings, called interpolative Reich-Rus-Ćirić type proximal contractions of the first and second kinds. Our purpose is to show that their results follow from a fixed point theorem for interpolative Reich-Rus-Ćirić type contraction mappings [E. Karapinar, R. Agarwal and H. Aydi, Interpolative Reich-Rus-Ćirić contractions on partial metric spaces, Mathematics 6 (2018), 7 pages]. [ABSTRACT FROM AUTHOR]

Recently, Altun et al. [1] introduced the notion of p-proximal contractions and p-proximal contractive mappings and discussed about best proximity point results for this two classes of mappings. After that, Gabeleh and Markin [3] showed that the best proximity point theorem for p-proximal contractions proved in [1] follows from the same conclusion fixed point theory. In this short note, we show that the best proximity point theorem for p-proximal contractive mappings follows from the corresponding fixed point result for metric spaces. [ABSTRACT FROM AUTHOR]

Very recently, I. Altun, M. Aslantas and H. Sahin [1] introduced the notion of p -proximal contractions and surveyed the existence of best proximity points for such class of non-self mappings in metric spaces. In this note we show that this existence result is a straightforward consequence of the same conclusion in fixed point theory. [ABSTRACT FROM AUTHOR]

The purpose of this paper is twofold. Firstly, certain common fixed point theorems are established via φ-contractive multivalued mappings involving point-dependent control functions as coefficients in the framework of complex valued metric spaces. Our results improve and extend several results in the existing literature. Moreover, this section is equipped by some illustrative examples in support of our results. Secondly, we point out some slip-ups in the examples of some recent papers based on multivalued contractive mappings in complex valued metric spaces. Our observations are also authenticated with the aid of some appropriate examples. Some rectifications to correct the erratic examples are also suggested. [ABSTRACT FROM AUTHOR]

In this short paper we show that the results obtained by [N. Hussain, V. Parvaneh, B. Samet and C. Vetro, Some fixed point theorems for generalized contractive mappings in complete metric spaces, Fixed Point Theory and Applications (2015) 2015:185] can be obtained without the continuity assumption for the self mapping. [ABSTRACT FROM AUTHOR]

This short and concise note provides a detailed exposition of the approach and results established by (Lin et al, 2015, pp.271-279). We show that the obtained results are not particularly surprising and new. Namely, using an old result due to K. Deimling it is indicated that tvs-cone metric spaces over solid cones are actually cone metric spaces over normal solid cones. Hence, there are only cone metric spaces over normal solid cones or over normal non-solid cones. One question still unanswered is whether an ordered topological vector space with a non-normal non-solid cone exists. [ABSTRACT FROM AUTHOR]

We show that the result on cyclic weak contractions of Harjani et al. (J. Nonlinear Sci. Appl. 6:279-284, ) holds without the assumption of compactness of the underlying space, and also without the assumption of continuity of the given mapping. [ABSTRACT FROM AUTHOR]

Muhammad Arshad, Aftab Hussain and Akbar Azam (Fixed point of ff-Geraghty contraction with applications, U.P.B. Sci. Bull., Series A, Vol. 78, Iss. 2, 2016) improved the notion of ff-Geraghty contraction type mappings and established some common fixed point theorems for a pair of ff-admissible mappings under the improved notion of ff-Geraghty contraction type condition in a complete metric space. But we observe some gaps in the proof of some theorems in the paper due to some insufficiency in the defining condition of the associated contraction mappings. The aim of this paper is to attempt to bridge the gaps by proposing some modifications in the contraction condition of the mappings. [ABSTRACT FROM AUTHOR]

Several recent papers in digital topology have sought to obtain fixed point results by mimicking the use of tools from classical topology, such as complete metric spaces. We show that in many cases, researchers using these tools have derived conclusions that are incorrect, trivial, or limited. [ABSTRACT FROM AUTHOR]

The aim of this paper is to present some new observations about w-distance (in the sense of O. Kada, T. Suzuki, W. Takahashi, Nonconvex minimization theorems and fixed point theorems in complete metric spaces, Math. Japonica 44, 2 (1996), 381-391) and F-contractions (in the sense of D. Wardowski, Fixed points of a new type of contractive mappings in complete metric spaces, Fixed Point Theory Appl., 2012:94 (2012)). Both concepts have been examined separately a lot, but there have been few attempts to connect them. This article is a step in filling this gap. Besides, some comments and improvements of results in the existing literature are presented. [ABSTRACT FROM AUTHOR]

Recently, Erdal Karapinar ([8] Karapinar E., α - ψ- Geraghty contraction type mappings and some related fixed point results, Filomat, 28:1 37-48 (2014)) introduced the notion of generalized α - ψ- Geraghty contraction type mappings in the setting of a metric space and proved the existence and uniqueness of a fixed point of such mappings. But we observe that the condition (H1) for the uniqueness of the fixed point of such mappings as proposed by Karapinar is not enough. The aim of this paper is to attempt to rectify it by proposing a slightly stronger condition in place of condition (H1). [ABSTRACT FROM AUTHOR]

Abstract: Huang and Zhang reviewed cone metric spaces in 2007 [Huang Long-Guang, Zhang Xian, Cone metric spaces and fixed point theorems of contractive mappings, J. Math. Anal. Appl. 332 (2007) 1468–1476]. We shall prove that there are no normal cones with normal constant and for each there are cones with normal constant . Also, by providing non-normal cones and omitting the assumption of normality in some results of [Huang Long-Guang, Zhang Xian, Cone metric spaces and fixed point theorems of contractive mappings, J. Math. Anal. Appl. 332 (2007) 1468–1476], we obtain generalizations of the results. [Copyright &y& Elsevier]

In [1], the author proved a fixed point theorem in cone metric spaces. In this paper, we show that that [1, Theorem 1] is a consequence of [1, Corollary 1]. [ABSTRACT FROM AUTHOR]

In this paper, we prove the existence and uniqueness of common fixed point of tower type contractive mappings in complete metric (pseudo)modular spaces involving the theoretic relation. However, the newly introduced contraction in this paper further characterize and includes in their full strength several existing results in metrical fixed point theory. Some nontrivial supportive examples were given to justify our result. Our results generalize, improve, and unify some existing results. [ABSTRACT FROM AUTHOR]

In this paper, a large class of contractions is studied that contains Banach and Matkowski maps as particular cases. Sufficient conditions for the existence of fixed points are proposed in the framework of b-metric spaces. The convergence and stability of the Picard iterations are analyzed, giving error estimates for the fixed-point approximation. Afterwards, the iteration proposed by Kirk in 1971 is considered, studying its convergence, stability, and error estimates in the context of a quasi-normed space. The properties proved can be applied to other types of contractions, since the self-maps defined contain many others as particular cases. For instance, if the underlying set is a metric space, the contractions of type Kannan, Chatterjea, Zamfirescu, Ćirić, and Reich are included in the class of contractivities studied in this paper. These findings are applied to the construction of fractal surfaces on Banach algebras, and the definition of two-variable frames composed of fractal mappings with values in abstract Hilbert spaces. [ABSTRACT FROM AUTHOR]

In this paper, we studied the properties of generalized John domains in metric space. We prove that a domain D is a φ-John domain if, and only if, D∖P is a φ′-John domain, where P is a subset of D containing finitely many points of D. Meanwhile, we also showed that the union of φ-John domains is a φ″-John domain in metric space. [ABSTRACT FROM AUTHOR]

In this paper, we primarily focused on the existence and uniqueness of the initial value problem for fractional order fuzzy ordinary differential equations in a fuzzy metric space. First, definitions and relevant properties of the Gamma function and Beta function within a fuzzy metric space were provided. Second, by employing the principle of fuzzy compression mapping and Choquet integral of fuzzy numerical functions, we established the existence and uniqueness of solutions to initial value problems for fuzzy ordinary differential equations. Finally, several examples were presented to demonstrate the validity of our obtained results. [ABSTRACT FROM AUTHOR]

In the present paper, under certain assumptions, we establish the convergence of iterates for self-mappings of complete metric spaces with graphs which are of a contractive type. The class of mappings considered in the paper contains the so-called cyclical mappings introduced by W. A. Kirk, P. S. Srinivasan and P. Veeramani in 2003 and the class of monotone nonexpansive operators. Our results hold in the case of a symmetric graph. [ABSTRACT FROM AUTHOR]

In [1] Kohli and Vashistha gave an analogue of probabilistic version of Pant's Theorem ([2], Theorem 1). We note that mappings defined in Examples 3.6 to 3.8 of [1] are not self maps as claimed in the Definitions 3.1 and 3.2. In this context, we provide some relevant examples to complete the interesting results. [ABSTRACT FROM AUTHOR]

This paper delves into fixed point findings within a complete partially ordered b-metric space, focusing on mappings that adhere to weakly contractive conditions in the presence of essential topological characteristics. These findings represent modifications of established results and further extend analogous outcomes in the existing literature. The conclusions are substantiated by illustrative examples that strengthen the conclusion of the paper. [ABSTRACT FROM AUTHOR]

In this paper, we investigate the Besov space and the Besov capacity and obtain several important capacitary inequalities in a strictly local Dirichlet space, which satisfies the doubling condition and the weak Bakry–Émery condition. It is worth noting that the capacitary inequalities in this paper are proved if the Dirichlet space supports the weak (1 , 2) -Poincaré inequality, which is weaker than the weak (1 , 1) -Poincaré inequality investigated in the previous references. Moreover, we first consider the strong subadditivity and its equality condition for the Besov capacity in metric space. [ABSTRACT FROM AUTHOR]

Comparison is a powerful tool for decision support. Many measures have been proposed for comparing two metric spaces, but they do not consider the data dispersion in each metric space. Furthermore, no dedicated measure has yet been proposed for comparing two metric spaces containing elements belonging to various subtypes of a global datatype. In order to attenuate the aforementioned limitations, this paper proposes a new technique for comparing two metric spaces. More formally, given a metric space X, histograms are used for performing a gradual analysis of the data dispersion inside the neighborhood of each element of X. This is a refinement of the neighborhoods' analysis realized in an existing work. Then, another existing technique is used for associating one hidden Markov model λ X with X such that λ X learns the bin values and the visual shapes of the histograms derived from the instances in X. Meta-data derived from λ X are then saved as the components of a descriptor vector X → associated with X. Finally, the comparison between two metric spaces is performed through the comparison of their respective associated descriptor vectors using existing distance or similarity measures between two vectors. The proposed approach inherits the accuracy and the efficiency of the existing techniques on which it relies. Therefore, the experiments realized in this paper are only intended to show how it can be used for comparing particular metric spaces containing geolocations or stars in the celestial sphere. [ABSTRACT FROM AUTHOR]

In response to the practice of rescue channel blocking and a shortage of emergency materials in the event of sudden significant disasters, a multi-UAV collaborative distribution scheme was designed based on the demand for rapid and accurate distribution of materials. This paper constructed a multi-UAV collaborative task assignment and routing problem with simultaneous delivery and pick-up and time windows (MVTARPSDPTW), considering the factors of UAV load, energy consumption, cargo quality, and volume to minimize the total cost of UAV distribution and the full penalty of the task, as well as optimizing the balance of UAV efficiency. This paper proposes a multi-objective, improved brainstorming optimization algorithm based on Pareto dominance (MIBSO) to solve the MVTARPSDPTW problem. With DTLZ4, DTLZ5, and DTLZ6 benchmarks, this work tests the algorithm performance according to the characteristic attributes of the model sought, selecting the four indicators of GD, the Spacing metric, HV, and IGD, concerning convergence, solution distribution, and comprehensive performance. Case validation is based on a COVID-19 scenario in Changchun, China, and the results show that the model algorithm designed in this paper has good performance and feasibility in convergence and distribution of reconciliation. Finally, the multi-UAV emergency material distribution solution provides practical, theoretical support for rescue tasks in sudden significant disasters. [ABSTRACT FROM AUTHOR]

Soft set theory has attracted many researchers from several different branches. Sound theoretical improvements are accompanied with successful applications to practical solutions of daily life problems. However, some of the attempts of generalizing crisp concepts into soft settings end up with completely equivalent structures. This paper deals with such a case. The paper mainly presents the metrizability of the soft topology induced by a soft metric. The soft topology induced by a soft metric is known to be homeomorphic to a classical topology. In this work, it is shown that this classical topology is metrizable. Moreover, the explicit construction of an ordinary metric that induces the classical topology is given. On the other hand, it is also shown that soft metrics are actually cone metrics. Cone metrics are already proven to be an unsuccessful attempt of generalizing metrics. These results clarify that most, if not all, properties of soft metric spaces could be directly imported from the related classical theory. The paper concludes with an application of the findings, i.e., a new soft fixed point theorem is stated and proven with the help of the obtained homemorphism. [ABSTRACT FROM AUTHOR]

In this paper, some properties of locally antisymmetrically connected spaces which are the localized version of the antisymmetrically connected T0-quasi-metric spaces constructed as the natural counterparts of connected complementary graphs, are presented in terms of asymmetric norms. According to that, we investigated some different aspects and examples of local antisymmetric connectedness in the framework of asymmetrically normed real vector spaces. Specifically, it is proved that the structures of antisymmetric connectedness and local antisymmetric connectedness coincide for the T0-quasi-metrics induced by the asymmetric norms which associate the theory of quasi-metrics with functional analysis. [ABSTRACT FROM AUTHOR]

In this short note we generalize, complement and improve recent result on multiplicative metric spaces established by R.P. Agarwal et al. [Ravi P. Agarwal, Erdal Karapinar and Bessem Samet: An essential remark on fixed point results on multiplicative metric spaces. [ABSTRACT FROM AUTHOR]

The main goal of this paper is to compare the proof of the existence and uniqueness of fixed points for T -contractive mappings in various metric spaces and different distances regarding some techniques in mathematical analysis. Also, several comparisons to show the efficiency of the obtained result will be considered. [ABSTRACT FROM AUTHOR]

Let X = {x1,...,xn} be a finite set endowed with a metric d . The matrix A = (d(xi, xj))nxn is called a distance matrix. In this paper we discuss about the minimum rank that can be achieved by an n x n distance matrix and prove that the rank of every 5 x 5 and 6 x 6 distance matrix is not less than 4. [ABSTRACT FROM AUTHOR]

The fundamental goal of our paper is to study θ-convex contractive mappings in metric spaces. We demonstrate some fixed point results for such mappings. Also, we give an application to integral equations of our results. Consequently, our results encompass numerous generalizations of the Banach contraction principle on metric space. [ABSTRACT FROM AUTHOR]

The paper contains a survey of several results from the author's papers and joint papers by the author and Zakharyan, both on the zero existence and approximation for single-valued and multivalued (α, β)-search functionals, and also on the zero existence preservation for parametric family of such functionals, under the parameter changing. Some corollaries of these results in the fixed point and coincidence theory of single-valued and multivalued mappings of metric spaces are also given. The comparison is provided with some known results by other authors. In the concluding part of the paper, we investigate the problem on the existence of a parameter-continuous single-valued branch of zeros for a parametric family of search functionals. A theorem on the existence of a solution of this problem is proved. [ABSTRACT FROM AUTHOR]

This paper studies presentations of the Sierpinski gasket as a final coalgebra for a functor on three categories of metric spaces with additional designated points. The three categories which we study differ on their morphisms: one uses short (non-expanding) maps, the second uses continuous maps, and the third uses Lipschitz maps. The functor in all cases is very similar to what we find in the standard presentation of the gasket as an attractor. It was previously known that the Sierpinski gasket is bilipschitz equivalent (though not isomorhpic) to the final coalgebra of this functor in the category with short maps, and that final coalgebra is obtained by taking the completion of the initial algebra. In this paper, we prove that the Sierpiniski gasket itself is the final coalgebra in the category with continuous maps, though it does not occur as the completion of the initial algebra. In the Lipschitz setting, we show that the final coalgebra for this functor does not exist. [ABSTRACT FROM AUTHOR]

Recently, the fixed-point theorem for fuzzy contractive mappings has been investigated within the framework of intuitionistic fuzzy metric-like spaces. This interesting topic was explored through the utilization of G-Cauchy sequences as defined by Grabiec. The aim of this study is to enhance the aforementioned results in a few aspects. Initially, the proof of the fixed-point theorem is simplified and condensed, allowing for potential generalization to papers focusing on similar fixed-point analyses. Furthermore, instead of G-Cauchy sequences, the classical Cauchy sequences proposed by George and Veeramani are examined, incorporating an additional condition on the fuzzy metric. Within this context, a solution to an old unresolved question posed by Gregory and Sapena is provided. The findings are reinforced by relevant examples. Finally, the introduced fuzzy metrics are applied to the field of image processing. [ABSTRACT FROM AUTHOR]

The aim of this paper is to establish some fixed point results for enriched Kannan-type mappings in convex metric spaces. We first give an affirmative answer to a recent Berinde and Păcurar's question (Remark 2.3) [J. Comput. Appl. Math., 386 (2021), 113217]. Furthermore, we establish the existence and uniqueness of fixed points for Suzuki-enriched Kannan-type mappings in the setting of convex metric spaces. Finally, we present an application to approximate the solution of the Volterra integral equations to support our results. [ABSTRACT FROM AUTHOR]

In this paper, we introduce the notion of unified interpolative contractions of the Reich–Rus–Ćirić type and give some results about the fixed points for these mappings in the framework of relational metric spaces. We present examples where the results of some previous research are not relevant. Also, we apply our results to solving problems related to nonlinear matrix equations, emphasizing their practical importance. [ABSTRACT FROM AUTHOR]

After the initiation of Jachymski's contraction principle via digraph, the area of metric fixed point theory has attracted much attention. A number of outcomes on fixed points in the context of graph metric space employing various types of contractions have been investigated. The aim of this paper is to investigate some fixed point theorems for a class of nonlinear contractions in a metric space endued with a transitive digraph. The outcomes presented herewith improve, extend and enrich several existing results. Employing our findings, we describe the existence and uniqueness of a singular fractional boundary value problem. [ABSTRACT FROM AUTHOR]

In the present paper, we obtain three results on the existence of a fixed point for nonexpansive mappings. Two of them are generalizations of the result for F-contraction, while third one is a generalization of a recent result for set-valued contractions. [ABSTRACT FROM AUTHOR]

In this paper, we introduce two new classes of mixed (S,T)-α-admissible mappings and interspersed (S, g,T)-α-admissible mappings and study the sufficient conditions for the existence and uniqueness of a common fixed point of generalized (αs, ξ, ħ, τ)-Geraghty contractive mapping in the framework of partial b-metric spaces. We also provide two examples to show the applicability and validity of our results. Moreover, we present an application to the existence of solutions to an integral equation by means of one of our results. [ABSTRACT FROM AUTHOR]

In this paper, we introduce the concept of elliptic-valued b-metric spaces, extending the notions of elliptic-valued metric spaces and complex-valued metric spaces. We present several fixed-point results that involve rational and product terms within this novel space framework. To support our main findings, we offer numerical examples. Additionally, we demonstrate an application of Urysohn integral equations. [ABSTRACT FROM AUTHOR]

In the online facility assignment problem OFA (k , { c i } i = 1 k) , there exist k servers s 1 , ... , s k on a metric space where each s i has an integer capacity c i and a request arrives one-by-one. The task of an online algorithm is to irrevocably match a current request with one of the servers with vacancies before the next request arrives. As special cases for OFA (k , { c i } i = 1 k) , we consider OFA (k , { c i } i = 1 k) on a line , which is denoted by OFAL (k , { c i } i = 1 k) and OFAL eq (k , { c i } i = 1 k) , where the latter is the case of OFAL (k , { c i } i = 1 k) with equidistant servers. In this paper, we perform the competitive analysis for the above problems. As a natural generalization of the greedy algorithm grdy, we introduce a class of algorithms called MPFS (Most Preferred Free Servers) and show that any MPFS algorithm has the capacity-insensitive property, i.e., for any MPFS algorithm alg for OFA (k , { c i } i = 1 k) , if alg is c -competitive when c 1 = ⋯ = c k = 1 , then alg is c -competitive for general { c i } i = 1 k . By applying the capacity-insensitive property of the greedy algorithm grdy, we derive the matching upper and lower bounds 4 k − 5 on the competitive ratio of grdy for OFAL eq (k , { c i } i = 1 k). To investigate the capability of MPFS algorithms, we show that the competitive ratio of any MPFS algorithm alg for OFAL eq (k , { c i } i = 1 k) is at least 2 k − 1. Then, we propose a new MPFS algorithm idas (Interior Division for Adjacent Servers) for OFAL (k , { c i } i = 1 k) and show that the competitive ratio of idas for OFAL eq (k , { c i } i = 1 k) is at most 2 k − 1 , i.e., idas for OFAL eq (k , { c i } i = 1 k) is best possible in all the MPFS algorithms. We also give numerical experiments to investigate the performance of idas and grdy and show that idas performs better than grdy for distribution of request sequences with locality. [ABSTRACT FROM AUTHOR]

In this paper we prove gradient estimates of both elliptic and parabolic types, specifically, of Souplet-Zhang, Hamilton and Li-Yau types for positive smooth solutions to a class of nonlinear parabolic equations involving the Witten or drifting Laplacian on smooth metric measure spaces. These estimates are established under various curvature conditions and lower bounds on the generalised Bakry-Émery Ricci tensor and find utility in proving elliptic and parabolic Harnack-type inequalities as well as general Liouville-type and other global constancy results. Several applications and consequences are presented and discussed. [ABSTRACT FROM AUTHOR]

In this paper, we prove embedding theorems for the Möbius invariant space \mathcal {Q}_p on the open unit ball of \mathbb {C}^n into logarithmic tent spaces in the Bergman metric. [ABSTRACT FROM AUTHOR]