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In this article, we present some results on the existence and uniqueness of random solutions to a non-linear implicit fractional differential equation involving the generalized Caputo fractional derivative operator and supplemented with non-local and periodic boundary conditions. We make use of the fixed point theorems due to Banach and Krasnoselskii to derive the desired results. Examples illustrating the obtained results are also presented.

The aim of this paper is to present an algorithm to solve frictional contact problems by considering the Coulomb's criterion. As it is known, the frictional contact problem using Coulomb's criterion has no minimization principle behind. However in order to use algorithms based on minimization methods, the frictional contact problem is written as an optimization one, more specifically as a sequence of Tresca contact problems. Moreover a family of regularization functions is introduced in order to regularize the non-smooth character of the Tresca criterion, which in some cases can have an experimental justifications. As each minimization problem becomes smooth enough, the interior point method is used to solve the generated optimization problem.

This paper studies the existence and uniqueness of equilibrium prices in a model of the banking sector in which banks trade contingent convertible bonds with stock price triggers among each other. This type of financial product was proposed as an instrument for stabilizing the global banking system after the financial crisis. Yet it was recognized early on that these products may create circularity problems in the definition of stock prices—even in the absence of trade. We find that, if conversion thresholds are such that bond holders are indifferent about marginal conversions, there exists a unique equilibrium irrespective of the network structure. When thresholds are lower, the existence of equilibrium breaks down, whereas higher thresholds may lead to multiplicity of equilibria. Moreover, there are complex network effects. One bank’s conversion may trigger further conversions—or prevent them, depending on the constellations of asset values and conversion triggers.

In this work, we propose a new iterative method on Hadamard spaces, a modified version of the shrinking projection method. It can be regarded as a corresponding method to Mann's. We compare the proposed method with Mann's and discuss the efficiency of approximating a fixed point of mapping.

It is defined a class of generalized nonexpansive mappings, which properly contains those defined by Suzuki in 2008, and that preserves some of its fixed point results.

We address the exact boundary controllability of the semilinear wave equation $\partial_{tt}y-\Delta y + f(y)=0$ posed over a bounded domain $\Omega$ of $\mathbb{R}^d$. Assuming that $f$ is continuous and satisfies the condition $\limsup_{\vert r\vert\to \infty} \vert f(r)\vert /(\vert r\vert \ln^p\vert r\vert)\leq \beta$ for some $\beta$ small enough and some $p\in [0,3/2)$, we apply the Schauder fixed point theorem to prove the uniform controllability for initial data in $L^2(\Omega)\times H^{-1}(\Omega)$. Then, assuming that $f$ is in $\mathcal{C}^1(\mathbb{R})$ and satisfies the condition $\limsup_{\vert r\vert\to \infty} \vert f^\prime(r)\vert/\ln^p\vert r\vert\leq \beta$, we apply the Banach fixed point theorem and exhibit a strongly convergent sequence to a state-control pair for the semilinear equation.

Thispaper recognizes a general approach related to recent fixed point results about the classes of interpolative and hybrid contractions in metric space and general metric spaces. Considering auxiliary functions, so called Wardowski functions, and a rich set of implicit relations, we introduce types of(αvq,ϕ,F)−contractions andr−order hybrid(αvq,ϕ,F)−contractions in the setting ofb−metric-like spaces. They generate and simplify many forms of contractions widely used in the literature. The resulting theorems significantly extend, generalize, and unify an excellent work on fixed point theory.

This manuscript contains several new notions including intuitionistic fuzzyNbmetric space, intuitionistic fuzzy quasi-Sb-metric space, intuitionistic fuzzy pseudo-Sb-metric space, intuitionistic fuzzy quasi-N-metric space and intuitionistic fuzzy pseudoNbfuzzy metric space. We prove decomposition theorem and fixed-point results in the setting of intuitionistic fuzzy pseudoNbfuzzy metric space. Further, we provide several non-trivial examples to show the validity of introduced notions and results. At the end, we solve an integral equation, system of linear equations and nonlinear fractional differential equations as applications.

This article introduces the concept of partially controlled J metric spaces; in particular, the J metric space with self-distance is not necessarily zero, which is important in computer science. We prove the existence of a unique fixed point for linear and nonlinear contractions, provide some examples to prove the existence of this metric space, and present some important applications in fractional differential equations, i.e., “Riemann–Liouville derivatives”.

The aim of this paper is to give some fixed point results in generalized Menger probabilistic metric spaces. Moreover, some nontrivial examples are presented to illustrate the superiority of the obtained results. In addition, several interesting applications are given to show that our results are meaningful and valuable.

In this paper, our aim is to provide new solutions to some open problems given in [18] and [27] about the discontinuity at fixed point and related results. For this purpose, we prove new theorems and corollaries using simulation functions and known fixed-point techniques. Publisher's Version

In this work, a family of piecewise chaotic maps is proposed. This family of maps is parameterized by the nonlinear functions used for each piece of the mapping, which can be either symmetric or non-symmetric. Applying a constraint on the shape of each piece, the generated maps have no equilibria and can showcase chaotic behavior. This family thus belongs to the category of systems with hidden attractors. Numerous examples of chaotic maps are provided, showcasing fractal-like, symmetrical patterns at the interchange between chaotic and non-chaotic behavior. Moreover, the application of the proposed maps to a pseudorandom bit generator is successfully performed.

We investigate fixed points for p cyclic maps by introducing a new notion of p–cyclic infimum summing maps and a generalized best proximity point for p–cyclic maps. The idea generalizes some results about best proximity points in order to widen the class of sets and maps for which we can ensure the existence and uniqueness of best proximity points. The replacement of the classical notions of best proximity points and distance between the consecutive set arises from the well-known group traveling salesman problem and presents a different approach to solving it. We illustrate the new result with a map that does not satisfy the known results about best proximity maps for p–cyclic maps.

This manuscript contains several fixed point results for αΓ-F-fuzzy contractive mappings in the framework of orthogonal fuzzy metric spaces. The symmetric property guarantees that the distance function is consistent and does not favour any one direction in orthogonal fuzzy metric spaces. No matter how the points are arranged, it enables a fair assessment of the separations between all of them. In fixed point results, the symmetry condition is preserved for several types of contractive self-mappings. Moreover, we provide several non-trivial examples to show the validity of our main results. Furthermore, we solve non-linear fractional differential equations, the Atangana–Baleanu fractional integral operator and Fredholm integral equations by utilizing our main results.

In this paper, we introduce the concept of bicomplex-valued controlled metric spaces and prove fixed point theorems. Our results mainly focus on generalizing and expanding some recently established results. Finally, we explain an application of our main result to a certain type of fractional differential equation.

The aim of this manuscript is to introduce a novel concept called Jaggi-type hybrid (ϕ -F)-contraction and establish some fixed point results for this class of contractions in the framework of G-metric space. The validity of the main result is shown by a suitable example and the realized improvements with respect to the corresponding literature are highlighted. By using the constructed example, it is observed that the results established herein cannot be deduced from their analogs in previously announced results in the literature. As an application, the existence and uniqueness of solutions to certain nonlinear Volterra integral equations are investigated to illustrate the utility of our obtained results.

In this article, we develop a new notion that combines fixed-point theory and graph theory: graphical bipolar b-metric spaces. We demonstrate fixed-point solutions in the framework of graphical bipolar b-metric spaces, employing covariant and contravariant mapping contractions, which is a new addition to this end. This article also features illustrative examples drawn from various contexts to further demonstrate our findings. This is a significant study since it melds ideas from graph theory with those from generalized bipolar metric spaces, and considers that the symmetry of the edges of the underlying graphs connected with the enunciated metric spaces is essential in the graphical metric spaces.

The idea of enriched mappings in normed spaces is relatively a newer idea. In this paper, we initiate the study of enriched mappings in modular function spaces. We first introduce the concepts of enriched ρ-contractions and enriched ρ-Kannan mappings in modular function spaces. We then establish some Banach Contraction Principle type theorems for the existence of fixed points of such mappings in this setting. Our results for enriched ρ-contractions are generalizations of the corresponding results from Banach spaces to modular function spaces and those from contractions to enriched ρ-contractions. We make a first ever attempt to prove existence results for enriched ρ-Kannan mappings and deduce the result for ρ-Kannan mappings. Note that even ρ-Kannan mappings in modular function spaces have not been considered yet. We validate our main results by examples.

The paper's main goal is to introduce a novel type of interpolative convex contraction and build up some fresh findings for it using the interpolative convex contractions' progressive approach. We have established certain conclusions using orbitally S-complete and Suzuki type contractions in F-metric spaces. My research aims to examine the fixed point method's efficacy in solving fractional differential equation with boundary conditions.

This paper is concerned with the existence of solutions for a new boundary value problem of nonlinear coupled (k,ψ)–Hilfer fractional differential equations subject to coupled (k,ψ)–Riemann–Liouville fractional integral boundary conditions. We prove two existence results by applying the Leray–Schauder alternative, and Krasnosel’skiĭ’s fixed-point theorem under different criteria, while the third result, concerning the uniqueness of solutions for the given problem, relies on the Banach’s contraction mapping principle. Examples are included for illustrating the abstract results.

In this paper, we prove a fixed point result for F- contraction principle in the framework of rectangular M-metric space. An example is also adopted to exhibit the utility of our result. Finally, we apply our fixed point result to show the existence of solution of Fredholm integral equation.

In this paper, we introduce the notion of C*-algebra valued quasi metric space to generalize the notion of C*-algebra valued metric space and investigate the topological properties besides proving some core fixed point results. Finally, we employ our one of the main results to examine the existence and uniqueness of the solution for a system of Fredholm integral equations.

We discuss published assertions concerning fixed points in digital metric spaces that are incorrect or incorrectly proven, or reduce to triviality., 16 pages; 14 figures

In this paper, we study a class of fourth-order boundary value problems with integral boundary conditions. The nonlinearity may have time-singularity and change sign. Moreover, it satisfies general polynomial growth conditions. A new topological approach is applied to prove the existence of at least two nonnegative classical solutions. An example of application illustrates the existence result.

This paper provides a sufficient condition for the existence of solutions for generalized Nash equilibrium problems in the infinite-dimensional setting and with a countable (possibly infinite) number of players. The result has been achieved as a consequence of a modified version of Michael’s selection theorem that works even when the range space is not metrizable and the set-valued map has not closed values.

In this paper, inspired by the work of Muzeyyen Sangurlu Sezen [22] and H. Saleh Nasr et al. [20], we introduce ʘf -type controlled fuzzy metric spaces and establish some fixed point results in controlled fuzzy metric spaces. We provide suitable examples to validate our result. We also employ an application to substantiate the utility of our established result for fiding the unique solution of an integral equation emerging in the dynamic market equilibrium aspects to economics.Subject Classification: 54H25, 47H10, A11.

The purpose of this paper is to define the notion of extended convex ℱ contraction by imposing less conditions on the function ℱ satisfying certain contractive conditions. We prove the existence of fixed points for these types of mappings in the setting of b-metric spaces. In addition, some illustrative examples are provided to show the usability of the obtained results. Lastly, we use the obtained fixed-point results to find the fractals with respect to the iterated function systems in the framework of b-metric spaces. Furthermore, the variables involved in the b-metric space are symmetric, and symmetry plays an important role in solving the nonlinear problems defined in operator theory.

Since 1964, when I.A. Perov introduced the so-called generalized metric space where d(x,y) is an element of the vector space Rm, many researchers have considered various contractive conditions in this type of space. In this paper, we generalize, extend and unify some of those established results. We are primarily concerned with examining the existence of a fixed point of some mapping from X to itself, but if (x,y) belongs to some relation R on the set X, then the binary relation R and some F contraction defined on the space cone Rm are combined. We start our consideration with the recently announced results and give them strict, critical remarks. In addition, we improve several announced results by weakening some of the given conditions.

Today, two distinct camps exist in the Physics community: those who believe in the asymptotic safe gravity program for gravity, and those who don’t. Not many physicists are undecided, even if those who claim not to care. It is a polarizing topic, and nobody seems to ever be really convinced by the arguments of the others. Add to this, the existential threat potentially posed by asymptotic safety to the physicality of supersymmetry, supergravity, superstrings, M-Theory, and many of the popular GUTs and TOEs out there, and one can understand why the question of asymptotic safety of gravity is often either viewed as critical, or dismissed as irrelevant. Yet, the asymptotic safety program has claimed indications that gravity may be asymptotically safe. So far, none are definitive, and most are derided by the other camp. In the context of the multi-fold theory, we have shown that multi-fold gravity is asymptotically safe. Using arguments, that gravity is 2D at small scales, something agreed upon by most consistent theories of quantum gravity, we inferred that gravity is most probably asymptotically safe, even in non-muti-fold universes, and yet, we could manage to save superstrings as relevant around that 2D regime, while (mathematically) living in a tangent dual space. More recent results reinterpret the double copy duality and behavior of Yang Mills scattering to i) defined new AdS/CFT dualities, ii) encounter gravity as part of Yang Mills theory, iii) and encounter the multi-fold theory in both Yang Mills Actions, and in M-theory, through the AdS/CFT correspondence conjecture. Part of these previous works led us to announce that the AdS/CFT correspondence conjecture implies that General Relativity (GR) – based gravity is indeed asymptotically safe in a 4D spacetime. In the present paper, we detail such a non-perturbative derivation for GR-based gravity, and for GR-based gravity with. It does not require faith into evolution of time series, 2D processes, nor a priori multi-fold assumptions. In other words, the proof applies to Einstein gravity, in general, for conventional Physics, as well as for multi-fold universes. The paper also discusses considerations on why arguments, presented so far, against the asymptotic safety of gravity program would have been flawed, and, in particular, it shows how our proof is not affected by the Gribov ambiguity concerns, which does not apply to gravity + SM or SMG matter. Also supersymmetric matter are not asymptotically safe in 4D. Higher dimensions are also confirmed incompatible., Cite as: Stephane H Maes, (2022), "A Non-perturbative Proof of the Asymptotic Safety of 4D Einstein Gravity, With or Without Matter", https://doi.org/10.5281/zenodo.7953796, https://shmaesphysics.wordpress.com/2022/05/04/a-non-perturbative-proof-of-the-asymptotic-safety-of-4d-einstein-gravity-with-or-without-matter/, May 4, 2022.

In this paper, we introduce controlled S-metric-type spaces and give some of their properties and examples. Moreover, we prove the Banach fixed point theorem and a more general fixed point theorem in this new space. Finally, using the new results, we give two applications on Riemann–Liouville fractional integrals and Atangana–Baleanu fractional integrals.

Phase transitions with spontaneous symmetry breaking are expected for group field theories as a basic feature of the geometogenesis scenario. The following paper aims to investigate the equilibrium phase for group field theory by using the ergodic hypothesis on which the Gibbs-Boltzmann distributions must break down. The breaking of the ergodicity can be considered dynamically, by introducing a fictitious time inducing a stochastic process described through a Langevin equation, from which the randomness of the tensor field will be a consequence. This type of equation is considered particularly for complex just-renormalizable Abelian model of rank $d=5$, and we study some of their properties by using a renormalization group considering a coarse-graining both in time and space., Comment: 76 pages, 18 figures

In this paper, the notion of generalized quasi-weakly contractive operators in metric-like spaces is introduced, and new conditions for the existence of fixed points for such mappings are investigated. A non-trivial example which highlights the novelty of our principal idea is constructed. It is observed comparatively that the proposed concepts herein subsume some important results in the corresponding literature. As an application, one of our obtained findings is utilized to setup novel criteria for the existence of solutions to two-point boundary value problems of a second order differential equation. To attract new researchers in the directions examined in this article, a significant number of corollaries are pointed out and discussed.

The fixed-circle issue is a geometric technique that is connected to the study of geometric characteristics of certain points, and that are fixed by the self-mapping of either the metric space or of the generalized space. The fixed-disc problem is a natural resultant that arises as a direct outcome of this problem. In this study, our goal is to examine new classes of self-mappings that meet a new particular sort of contraction in a metric space. The common geometrical characteristic of the set of fixed points of any element of these classes is that a circle or even a disc, that is either termed the fixed circle or even the fixed disc of the appropriate self-map, is included within that set. In order to accomplish this, we establish two new classifications of contraction mapping: Fc-contractive mapping and Fc-expanding mapping. In the investigation of neural networks, activation functions with either fixed circles (or even fixed discs) are observed frequently. This demonstrates how successful our results with the fixed-circle (respectively, the fixed-disc) model were.

In this paper, we introduce the concept of fuzzy-controlled bipolar metric space and prove some fixed-point theorems in this space. Our results generalize and expand some of the literature’s well-known results. We also provide some applications of our main results to integral equations. The authors thank the Basque Government for its support of this study through grant IT1555-22.

The applications of non-zero self distance function have recently been discovered in both symmetric and asymmetric spaces. With respect to invariant point results, the available literature reveals that the idea has only been examined for crisp mappings in either symmetric or asymmetric spaces. Hence, the aim of this paper is to introduce the notion of invariant points for non-crisp set-valued mappings in metric-like spaces. To this effect, the technique of κ-contraction and Feng-Liu’s approach are combined to establish new versions of intuitionistic fuzzy functional equations. One of the distinguishing ideas of this article is the study of fixed point theorems of intuitionistic fuzzy set-valued mappings without using the conventional Pompeiu–Hausdorff metric. Some of our obtained results are applied to examine their analogues in ordered metric-like spaces endowed with an order and binary relation as well as invariant point results of crisp set-valued mappings. By using a comparative example, it is observed that a few important corresponding notions in the existing literature are complemented, unified and generalized.

In this article, we introduce the concept of weak Fℜm,η-contractions on relation-theoretic m-metric spaces and establish related fixed point theorems, where η is a control function and ℜ is a relation. Then, we detail some fixed point results for cyclic-type weak Fℜm,η-contraction mappings. Finally, we demonstrate some illustrative examples and discuss upper and lower solutions of Volterra-type integral equations of the form ξα=∫0αAα,σ,ξσmσ+Ψα,α∈0,1.

In this paper, we propose an alternated inertial projection algorithm for solving multi-valued variational inequality problem and fixed point problem of demi-contractive mapping. On one hand, this algorithm only requires the mapping is pseudo-monotone. On the other hand, this algorithm is combined with the alternated inertial method to accelerate the convergence speed. The global convergence of the algorithm can be obtained under mild conditions. Preliminary numerical results show that the convergence speed of our algorithm is faster than some existing algorithms.

We use numerical bootstrap techniques to study correlation functions of traceless symmetric tensors of $O(N)$ with two indexes $t_{ij}$. We obtain upper bounds on operator dimensions for all the relevant representations and several values of $N$. We discover several families of kinks, which do not correspond to any known model and we discuss possible candidates. We then specialize to the case $N=4$, which has been conjectured to describe a phase transition in the antiferromagnetic real projective model ARP$^{3}$. Lattice simulations provide strong evidence for the existence of a second order phase transition, while an effective field theory approach does not predict any fixed point. We identify a set of assumptions that constrain operator dimensions to a closed region overlapping with the lattice prediction. The region is still present after pushing the numerics in the single correlator case or when considering a mixed system involving $t$ and the lowest dimension scalar singlet., 49 pages, 27 figures Fixed minor typos. Added a subsection on "External operator as the lowest dimensional operator of its kind". Included bounds using this additional assumption in figures 8a and 8b

In this study, we initiate the concept of fuzzy L-R-contraction and establish some fixed point results involving a G-transitive binary relation and fuzzy L-simulation functions, by employing suitable hypotheses on a fuzzy metric space endowed with a binary relation. The presented results unify, generalize, and improve various previous findings in the literature.

In this paper, we obtain two common fixed point results for mappings satisfying the generalized (ψ,φ)-contractive type conditions given by a rational expression on a complete metric space. Our results generalize several well known theorems of the literature in the context of (ψ,φ)-rational contraction. In addition, there is an example for obtained results.

In this paper, we introduce a new class of generalized contractive mappings to establish a fixed point theorem for this class of mappings in complete quasimetric spaces. In fact, at first we present the notion of ordered cyclic weakly (ψ, ϕ, A, B)- contraction and then we establish a fixed point theorem for such mappings in complete ordered s-quasimetric spaces. This can be considered as an improvement of some old fixed point theorems in the literature. Finally, we provide an example to show that our result is genuine generalizations of some fixed point theorems. Publisher's Version

This article implements the idea of introducing the concept of C-weak-fuzzy contraction mapping in the framework of fuzzy cone metric spaces, and deriving some unique common fixed point results. A nontrivial example is enunciated to uphold our results. Our results unify, enrich and extend some pioneer results in the existing literature in the fuzzy setting. In the end, an application to Fredholm nonlinear integral equation is offered showing the superiority of our results, which is in turn supported by an example. Publisher's Version

We introduce an arithmetic functional equation f(x2+y2)=f(x2)+f(y2) and then investigate stability estimates of the functional equation by using the Brzdȩk fixed point theorem on a non-Archimedean fuzzy metric space and a non-Archimedean fuzzy normed space. To apply the Brzdȩk fixed point theorem, the proof uses the linear relationship between two variables, x and y.

We study the Kelvinons: monopole ring solutions to the Euler equations, regularized as the Burgers vortex in the viscous core. There is finite anomalous dissipation in the inviscid limit. However, in the anomalous Hamiltonian, some terms are growing as logarithms of Reynolds number; these terms come from the core of the Burgers vortex. In our theory, the turbulent multifractal phenomenon is similar to asymptotic freedom in QCD, with these logarithmic terms summed up by an RG equation. The small effective coupling does not imply small velocity; on the contrary, velocity is large compared to its fluctuations, which opens the way for a quantitative theory. In the leading order in the perturbation theory in this effective coupling constant, we compute running multifractal dimensions for high moments of velocity circulation, in good agreement with the data for quantum Turbulence and available data for classical Turbulence. The logarithmic dependence of fractal dimensions on the loop size comes from the running coupling in anomalous dimensions. This slow logarithmic drift of fractal dimensions would be barely observable at Reynolds numbers achievable at modern DNS., Comment: 32 pages, 8 figures. arXiv admin note: text overlap with arXiv:2209.12312, revised topological analysis, revised energy balance analysis, a new analysis of multifractal laws with logarithmic corrections, added visualization of the Kelvinon velocity field and Q&A section; added the section with discussion of two phases of Turbulence

In this paper, we study a fixed-point problem with a set-valued mapping by using an algorithm based on unions of nonexpansive mappings. We show that an approximate solution is reached after a finite number of iterations in the presence of computational errors. This result is an extension of the results known in the literature.

We introduce the novel concept of (α-ψ)-fuzzy contractive mappings on fuzzy double-controlled metric spaces and demonstrate some fixed-point results. The theorems presented generalize some intriguing findings in the literature. Thus, we prove the fixed-point theorem in the settings of fuzzy double-controlled metric spaces. Furthermore, we provide several examples and an application of our result on the existence of the solution to an integral equation.

In this paper, we introduce and study a new class of coupled and uncoupled systems, consisting of mixed-type ψ1-Hilfer and ψ2-Caputo fractional differential equations supplemented with asymmetric and symmetric integro-differential nonlocal boundary conditions (systems (2) and (13), respectively). As far as we know, this combination of ψ1-Hilfer and ψ2-Caputo fractional derivatives in coupled systems is new in the literature. The uniqueness result is achieved via the Banach contraction mapping principle, while the existence result is established by applying the Leray–Schauder alternative. Numerical examples illustrating the obtained results are also presented.

In this paper, we introduce the new notion of contravariant (α−ψ) Meir–Keeler contractive mappings by defining α-orbital admissible mappings and covariant Meir–Keeler contraction in bipolar metric spaces. We prove fixed point theorems for these contractions and also provide some corollaries of main results. An example is also be given in support of our main result. In the end, we also solve an integral equation using our result.

In this paper, we will prove several new results related to the concept of the multi-valued Feng–Liu contraction. An existence, approximation and localization fixed point theorem for a generalized multi-valued nonself Feng–Liu contraction and a new fixed point theorem for multi-valued Feng–Liu contractions in vector-valued metric spaces are proved. Stability results and an application to a system of operatorial inclusions are also given.

In this paper, we introduce an iteration process to approximate a fixed point of a contractive self-mapping. The comparison theorem indicates that our iteration process is faster than the other existing iteration processes in the literature. We also obtain convergence and stability theorems of this iterative process for a contractive self-mapping. Numerical examples show that our iteration process for approximating a fixed point of a contractive self-mapping is faster than the existing methods. Based on this process, we finally present a new modified Newton-Raphson method for finding the roots of a function and generate some nice polynomiographs.