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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.

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.

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.

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 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.

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 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 and study a new class of boundary value problems, consisting of a mixed-type ψ1-Hilfer and ψ2-Caputo fractional order differential equation supplemented with integro-differential nonlocal boundary conditions. The uniqueness of solutions is achieved via the Banach contraction principle, while the existence of results is established by using the Leray–Schauder nonlinear alternative. Numerical examples are constructed illustrating the obtained results.

In this paper, under some new appropriate conditions imposed on the parameters and mappings involved in the proximal mapping associated with a general H-monotone operator, its Lipschitz continuity is proved and an estimate of its Lipschitz constant is computed. The main contribution of this work is the establishment of a new equivalence relationship between the graph convergence of a sequence of general strongly H-monotone mappings and their associated proximal mappings, respectively, to a given general strongly H-monotone mapping and its associated proximal mapping by using the notions of graph convergence and proximal mapping concerning a general strongly H-monotone mapping. By employing the concept of proximal mapping relating to general strongly H-monotone mapping, some iterative algorithms are proposed, and as an application of the obtained equivalence relationship mentioned above, a convergence theorem for approximating a common element of the set of solutions of a system of generalized variational inclusions involving general strongly H-monotone mappings and the set of fixed points of an ({an},{bn},ϕ)-total uniformly L-Lipschitzian mapping is proved. It is significant to emphasize that our results are new and improve and generalize many known corresponding results.

One of the latest techniques in metric fixed point theory is the interpolation approach. This notion has so far been examined using standard functional equations. A hybrid form of this concept is yet to be uncovered by observing the available literature. With this background information, and based on the symmetry and rectangular properties of generalized metric spaces, this paper introduces a novel and unified hybrid concept under the name interpolative Y-Hardy–Rogers–Suzuki-type Z-contraction and establishes sufficient conditions for the existence of fixed points for such contractions. As an application, one of the obtained results was employed to examine new criteria for the existence of a solution to a boundary valued problem arising in the oscillation of a spring. The ideas proposed herein advance some recently announced important results in the corresponding literature. A comparative example was constructed to justify the abstractions and pre-eminence of our obtained results.

Gregori and Romaguera introduced, in 2004, the notion of a KM-fuzzy quasi-metric space as a natural asymmetric generalization of the concept of fuzzy metric space in the sense of Kramosil and Michalek. Ever since, various authors have discussed several aspects of such spaces, including their topological and (quasi-)metric properties as well as their connections with domain theory and their relationship with other fuzzy structures. In particular, the development of the fixed point theory for these spaces and other related ones, such as fuzzy partial metric spaces, has received remarkable attention in the last 15 years. Continuing this line of research, we here establish general fixed point theorems for left and right complete Hausdorff KM-fuzzy quasi-metric spaces, which are applied to deduce characterizations of these distinguished kinds of fuzzy quasi-metric completeness. Our approach, which mixes conditions of Suzuki-type with contractions of α−ϕ-type in the well-known proposal of Samet et al., allows us to extend and improve some recent theorems on complete fuzzy metric spaces. The obtained results are accompanied by illustrative and clarifying examples.

We investigate the existence and uniqueness results for coupled Langevin differential equations of fractional order with Katugampola integral boundary conditions involving generalized Liouville–Caputo fractional derivatives. Furthermore, we discuss Ulam–Hyers stability in the context of the problem at hand. The results are shown with examples. Results are asymmetric when a generalised Liouville–Caputo fractional derivative (ρ) parameter is changed. With its novel results, this paper makes a significant contribution to the relevant literature.

In this work, we introduce a new type of generalized mixed-type quadratic-additive functional equation and obtain its general solution. The main goal of this work is to investigate Ulam stability of this mixed type of quadratic-additive functional equation in the setting of non-Archimedean fuzzy φ-2-normed space and non-Archimedean Banach space using the direct and fixed point approaches by taking into our account two cases: even mapping and odd mapping.

In this paper, we introduce the new concept of mutual Reich contraction that involves a pair of operators acting on a distance space. We chose the framework of strong b-metric spaces (generalizing the standard metric spaces) in order to add a more extended underlying structure. We provide sufficient conditions for two mutually Reich contractive maps in order to have a common fixed point. The result is extended to a family of operators of any cardinality. The dynamics of iterative discrete systems involving this type of self-maps is studied. In the case of normed spaces, we establish some relations between mutual Reich contractivity and classical contractivity for linear operators. Then, we introduce the new concept of mutual functional contractivity that generalizes the concept of classical Banach contraction, and perform a similar study to the Reich case. We also establish some relations between mutual functional contractions and Banach contractivity in the framework of quasinormed spaces and linear mappings. Lastly, we apply the obtained results to convolutional operators that had been defined by the first author acting on Bochner spaces of integrable Banach-valued curves.

In a personal communication, Prof. Domínguez Benavides noted that a fixed-point theorem for modular nonexpansive mappings in Lp(·)(Ω) obtained under the assumptions p+1. Therefore, the conclusion is well known. In this note, we establish said conclusion without the assumption p+

In the present work, we have introduced a new type of (ξ,ω)-weakly cyclic generalized contraction in the setting of metric spaces and established some fixed-point results. Fixed-point results are useful in establishing the existence of unique solution to differential equations. We have supplemented the derived results with suitable non-trivial examples with an application to the Boundary Value Problem, generalizing some known results. The analytical result has been verified with numerical simulation.

Let X be a linear space over K∈{R,C}, Y be a real or complex Banach space and f:Xn→Y. With some fixed aji,Ci1…in∈K (j∈{1,…,n}, i,ik∈{1,2}, k∈{1,…,n}), we study, using the direct and the fixed point methods, the stability and the general stability of the equation f(a11x11+a12x12,…,an1xn1+an2xn2)=∑1≤i1,…,in≤2Ci1…inf(x1i1,…,xnin), for all xjij∈X (j∈{1,…,n},ij∈{1,2}). Our paper generalizes several known results, among others concerning equations with symmetric coefficients, such as the multi-Cauchy equation or the multi-Jensen equation as well as the multi-Cauchy–Jensen equation. We also prove the hyperstability of the above equation in m-normed spaces with m≥2.

In algorithm development, symmetry plays a vital part in managing optimization problems in scientific models. The aim of this work is to propose a new accelerated method for finding a common point of convex minimization problems and then use the fixed point of the forward-backward operator to explain and analyze a weak convergence result of the proposed algorithm in real Hilbert spaces under certain conditions. As applications, we demonstrate the suggested method for solving image inpainting and image restoration problems.

By using a class of aggregation control functions, we introduce the concept of multiple-HU-OS1-stability and get an optimum approximation for a nonlinear single fractional differential equation (NS-ABC-FDE) with a Mittag–Leffler kernel. We apply an alternative fixed-point theorem to prove the existence of a unique solution and the multiple-HU-OS1-stability for the NS-ABC-FDE in the symmetric matrix-valued FBS. Finally, with an example, we show the application of the obtained results.

This paper focuses on the spherical fixed point set of a circle action on an ALE space endowed with Kronheimer's hyperkaehler metric. The induced metric on the sphere is described by using the algebraic geometry of rational curves on algebraic surfaces, in particular the lines on a cubic., Dedicated to the memory of Michael Atiyah

In our recent paper we obtained an extension of a theorem of Tam (2018), which was established for iterates of a set-valued paracontracting operators in a finite-dimensional Euclidean space. This extension was obtained for exact iterates of maps in a metric space. In the present paper we prove two analogs of this result for inexact iterates under the presence of computational errors. In the first result, the errors are summable, while for the second one they converge to zero. In a particular case of a Banach space, if all the operators are symmetric, then the set of all limit points of iterates is symmetric too.

For many fibred systems the existence of an invariant measure can be proved but considerably less is known about the shape of the density. In this note various examples of invariant densities are discussed: Piecewise fractional linear maps with four branches and maps which are associated to continued fractions with increasing digits. There are ergodic maps with a non-integrable density which do not have an indifferent fixed point and maps such that the set of points which miss the digit $k=1$ has positive Lebesgue measure.

The main purpose of this research is to establish a new generalized $ \xi^{\ast } $-Kannan type double controlled contraction on a sequence and obtain fixed point results for a pair of multivalued mappings in left $ K $-sequentially complete double controlled dislocated quasi metric type spaces. New results in different setting of generalized metric spaces and ordered spaces and also new results for graphic contractions can be obtained as corollaries of our results. An example is presented to show the novelty of results. In this paper, we unify and extend some recent results in the existing literature.

Using the approach of so-called c-sequences introduced by the fifth author in his recent work, we give much simpler and shorter proofs of multivalued Perov's type results with respect to the ones presented in the recently published paper by M. Abbas et al. Our proofs improve, complement, unify and enrich the ones from the recent papers. Further, in the last section of this paper, we correct and generalize the well-known Perov's fixed point result. We show that this result is in fact equivalent to Banach's contraction principle.

The goal of this study is to solve a non-linear matrix equation of the form $ \mathcal{X} = \mathcal{Q} + \sum\limits_{i = 1}^{m} \mathcal{B}_{i}^{*}\mathcal{G} (\mathcal{X})\mathcal{B}_{i} $, where $ \mathcal{Q} $ is a Hermitian positive definite matrix, $ \mathcal{B}_{i}^{*} $ stands for the conjugate transpose of an $ n\times n $ matrix $ \mathcal{B}_{i} $ and $ \mathcal{G} $ an order-preserving continuous mapping from the set of all Hermitian matrices to the set of all positive definite matrices such that $ \mathcal{G}(O) = O $. We explore the necessary and sufficient criteria for the existence of a unique positive definite solution to a particular matrix problem. For the said reason, we develop some fixed point results for $ \mathcal{FG} $-contractive mappings on complete metric spaces equipped with any binary relation (not necessarily a partial order). We give adequate examples to confirm the fixed-point results and compare them to early studies, as well as four instances that show the convergence analysis of non-linear matrix equations using graphical representations.

This paper deals with a well known open problem raised by Kannan (Bull. Calcutta Math. Soc., 60: 71–76, 1968) and B. E. Rhoades (Contemp. Math., 72: 233–245, 1988) on the existence of general contractions which have fixed points, but do not force the continuity at the fixed point. We propose some new affirmative solutions to this question using two new contractions called $ (\psi, \varphi) $-$ \mathcal{A} $-contraction and $ (\psi, \varphi) $-$ \mathcal{A^{\prime}} $-contraction inspired by the results of H. Garai et al. (Applicable Analysis and Discrete Mathematics, 14(1): 33–54, 2020) and P. D. Proinov (J. Fixed Point Theory Appl. (2020) 22: 21). Some new fixed point and common fixed point results in compact metric spaces and also in complete metric spaces are proved in which the corresponding contractive mappings are not necessarily continuous at their fixed points. Moreover, we show that new solutions to characterize the completeness of metric spaces. Several examples are provided to verify the validity of our main results.

In this article, the concept of a Hausdorff fuzzy $ b $-metric space is introduced. The new notion is used to establish some fixed point results for multivalued mappings in $ G $-complete fuzzy $ b $-metric spaces satisfying a suitable requirement of contractiveness. An illustrative example is formulated to support the results. Eventually, an application for the existence of a solution for an integral inclusion is established which involves showing the materiality of the obtained results. These results are more general and some theorems proved by of Shehzad et al. are their special cases.

In this paper, we study a boundary value problem consisting of Hahn integro-difference equation supplemented with four-point fractional Hahn integral boundary conditions. The novelty of this problem lies in the fact that it contains two fractional Hahn difference operators and three fractional Hahn integrals with different quantum numbers and orders. Firstly, we convert the given nonlinear problem into a fixed point problem, by considering a linear variant of the problem at hand. Once the fixed point operator is available, we make use the classical Banach's and Schauder's fixed point theorems to establish existence and uniqueness results. An example is also constructed to illustrate the main results. Several properties of fractional Hahn integral that will be used in our study are also discussed.

We introduce a new class of generalized graphic fuzzy $ F $- contractive mappings on metric spaces and establish the existence of common fuzzy coincidence and fixed point results for such contractions. It is significant to note that we do not use any form of continuity of mappings to prove these results. Some examples are provided to verify our proven results. Various developments in the existing literature are generalized and extended by our results. It is aimed that the initiated concepts in this work will encourage new research aspects in fixed point theory and related hybrid models in the literature of fuzzy mathematics.

The purpose of the present paper is to prove some fixed point results for cyclic-type operators in extended $ b $-metric spaces. The considered operators are generalized $ \varphi $-contractions and $ \alpha $-$ \varphi $ contractions. The last section is devoted to applications to integral type equations and nonlinear fractional differential equations using the Atangana-Bǎleanu fractional operator.

In this paper, we introduce the notion of a modular p-metric space (an extended modular b-metric space) and establish some fixed point results for alpha-nu-Meir-Keeler contractions in this new space. Using these results, we deduce some new fixed point theorems in extended modular metric spaces endowed with a graph and in partially ordered extended modular metric spaces. Also, we develop an important relation between fuzzy-Meir-Keeler and extended fuzzy p-metric with modular p-metric and get certain new fixed point results in triangular fuzzy p-metric spaces. We provide an example and an application to support our results which generalize several well known results in the literature., Basque GovernmentBasque Government [IT1207-19]; Ege University Scientific Research Projects Coordination UnitEge University [FGA-2020-22080], The authors would like to thank the editor and the anonymous referees for their careful reading of our manuscript and their many insightful comments and suggestions. The authors thank the Basque Government for its support of this work through Grant IT1207-19. This study is supported by Ege University Scientific Research Projects Coordination Unit. Project Number FGA-2020-22080.

We determine the common fixed point of two maps satisfying Hardy-Roger type contraction in a complete partial b-metric space without exploiting any variant of continuity or commutativity, which is indispensable in analogous results. Towards the end, we give examples and an application to solve a Cantilever beam problem employed in the distortion of an elastic beam in equilibrium to substantiate the utility of these improvements.

We give a new solution to the Rhoades' open problem on the discontinuity at fixed point via the notion of an S-metric. To do this, we develop a new technique by means of the notion of a Zamfirescu mapping. Also, we consider a recent problem called the "fixed-circle problem" and propose a new solution to this problem as an application of our technique., Balikesir University BAP 2018/019 BAP 2018/021

The fixed point results for Chatterjea type contraction in the setting of Complete metric space exists in literature. Taking this approach forward Karapinar gave the concept of cyclic Chatterjea contraction mappings. Fan also worked on these cyclic mappings in a new setting of quasi-partial b-metric space. Motivated by the work of these researchers, we have introduced the notion of $qp_{b}$-cyclic Chatterjea contractive mappings and established fixed point results on them. The aim of this paper is to use an interpolative approach in the framework of quasi-partial b-metric space and to prove existence and uniqueness of fixed point theorem for $qp_{b}$-interpolative Chatterjea contraction mappings. The results are affirmed with applications based on them.

In this paper, we prove the fixed-point theorem for rational contractive mapping on ®-metric space. Additionally, an Euclidean metric space with a binary relation example and an application to the first-order boundary value problem are given. Moreover, the obtained results generalize and extend some of the well-known results in the literature. © 2022 by the authors., Eusko Jaurlaritza: IT1207-19, The authors thank the Basque Government for its support of this work through Grant IT1207-19.

We discuss the solvability of a (p,q)-difference equation of fractional order α∈(1,2], equipped with anti-periodic boundary conditions involving the first-order (p,q)-difference operator. The desired results are accomplished with the aid of standard fixed point theorems. Examples are presented for illustrating the obtained results.

The aim of this paper is to approximate the fixed points of generalized α-nonexpansive mappings using AA-iterative algorithm. We establish some weak and strong convergence results for generalized α-nonexpansive mappings in uniformly convex Banach spaces. A numerical example is also given to show that the AA-iterative algorithm converges faster than some others algorithms for generalized α-nonexpansive mappings. Lastly, using the AA-iterative algorithm, we approximate the weak solution of delay composite functional differential equation of the Volterra–Stieltjes type.

In this article, we modify the symmetry of orthogonal metric spaces and we prove common fixed point theorems via simulation functions in orthogonal Rectangular metric spaces. We also provide an illustrative example to support our results. The derived results have been applied to find analytical solutions to integral equations. The analytical solutions are verified with a numerical simulation.

In this study, we examine the existence and Hyers–Ulam stability of a coupled system of generalized Liouville–Caputo fractional order differential equations with integral boundary conditions and a connection to Katugampola integrals. In the first and third theorems, the Leray–Schauder alternative and Krasnoselskii’s fixed point theorem are used to demonstrate the existence of a solution. The Banach fixed point theorem’s concept of contraction mapping is used in the second theorem to emphasise the analysis of uniqueness, and the results for Hyers–Ulam stability are established in the next theorem. We establish the stability of Ulam–Hyers using conventional functional analysis. Finally, examples are used to support the results. When a generalized Liouville–Caputo (ρ) parameter is modified, asymmetric results are obtained. This study presents novel results that significantly contribute to the literature on this topic.

In this study, we utilize the notion of triple controlled metric type space that preserves the symmetry property, which is a generalization of b-metric-type spaces, to prove new fixed-point results. We introduce (α-F)-contractive mappings and Θ-contractive mappings on triple controlled metric type space settings. Then, we establish the existence and uniqueness of fixed-point results on complete triple controlled metric type space. Moreover, some examples and applications to boundary-value problems of the fourth-order differential equation are presented to display the usage of the obtained result.

This work proposes the Enhanced Fixed Point Method (EFPM) as a straightforward modification to the problem of finding an exact or approximate solution for a linear or nonlinear algebraic equation. The proposal consists of providing a versatile method that is easy to employ and systematic. Therefore, it is expected that this work contributes to breaking the paradigm that an effective modification for a known method has to be necessarily long and complicated. As a matter of fact, the method expresses an algebraic equation in terms of the same equation but multiplied for an adequate factor, which most of the times is just a simple numeric factor. The main idea is modifying the original equation, slightly changing it for others in such a way that both have the same solution. Next, the modified equation is expressed as a fixed point problem and the proposed parameters are employed to accelerate the convergence of the fixed point problem for the original equation. Since the Newton method results from a possible fixed point problem of an algebraic equation, we will see that it is relatively easy to get modified versions of the Newton method with orders of convergence major than two. We will see in this work the convenience of this procedure.

The subject of this paper is the existence, uniqueness and stability of solutions for a new sequential Van der Pol–Duffing (VdPD) jerk fractional differential oscillator with Caputo–Hadamard derivatives. The arguments are based upon the Banach contraction principle, Krasnoselskii fixed-point theorem and Ulam–Hyers stabilities. As applications, one illustrative example is included to show the applicability of our results.

In this study, inspired by the concept of B-metric-like space (BMLS), we introduce the concept of orthogonal B-metric-like space (OBMLS) via a hybrid pair of operators. Additionally, we establish the concept of orthogonal dynamic system (ODS) as a generalization of the dynamic system (DS), which improves the existing results for analysies such as those presented here. By applying this, some new refinements of the F⊥-Suzuki-type (F⊥-ST) fixed-point results are presented. These include some tangible instances, and applications in the field of nonlinear analysis are given to highlight the usability and validity of the theoretical results.

We introduce and study a new class of nonlinear coupled Hilfer differential equations with nonlocal boundary conditions involving Riemann–Liouville and Hadamard-type iterated fractional integral operators. By applying the Leray–Schauder alternative and Krasnosel’skiĭ’s fixed point theorem, two results presenting different criteria for the existence of solutions to the given problem are proven. The third result provides a sufficient criterion for the existence of a unique solution to the problem at hand. Numerical examples are constructed to demonstrate the application of the results obtained. Two graphs show asymmetric solutions when a Hilfer parameter is varied. The work presented in this paper is novel and significantly enriches the literature on the topic.

In the present work, we establish fixed-point results for a pair of mappings satisfying some contractive conditions on rational expressions with coefficients as point-dependent control functions in the setting of tricomplex-valued metric spaces. The proven results are extension and generalisation of some of the literature’s well-known results. We also explore some of the applications to our key results.

In this article, we consider the non-linear semigroup of \textit{enriched Kannan} contractive mapping and prove the existence of common fixed point on a non-empty closed convex subset $\mathcal C$ of a real Banach space $\mathscr X$, having uniformly normal structure.