Search

Abstract Our reply on the above comment [1] shows that the new mapping method which proposed by Zeng and Yong [2] is absolutely right. Consequently, the solutions of the nonlinear evolution equations obtained in Zayed and Al-Nowehy [3,4] are true. Unfortunately, the author of this comment [1] failed in using this method and wrote a wrong comment. [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 paper aims to give an extended class of contractive mappings combining types of Suzuki contractions α-admissible mapping and Wardowski F-contractions in b-metric-like spaces. Our results cover and generalize many of the recent advanced results on the existence and uniqueness of fixed points and fulfill the Suzuki-type nonlinear hybrid contractions on various generalized metrics. [ABSTRACT FROM AUTHOR]

We construct a counterexample that disproves the claim of Theorem 0.2 of the paper “Injective mappings and solvable vector fields of Euclidean spaces”, which appeared in Topology Appl. 136 (2004), 261–274. [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]

In this paper, we introduce new types of contraction mappings named S-Pata-type contraction mapping and Generalized S-Pata-type contraction mapping in the framework of S-metric space. Then, we prove some new fixed-point results for S-Pata-type contraction mappings and Generalized S-Pata-type contraction mappings. To support our results, we provide examples to illustrate our findings and also apply these results to the ordinary differential equation to strengthen our conclusions. [ABSTRACT FROM AUTHOR]

We explore the intermixed method for finding a common element of the intersection of the solution set of a mixed variational inequality and the fixed point set of a nonexpansive mapping. We point out that Khuangsatung and Kangtunyakarn's statement [J. Inequal. Appl. 2023:1, 2023] regarding the resolvent utilized in their paper is not correct. To resolve this gap, we employ the epigraphical projection and the product space approach. In particular, we obtain a strong convergence theorem with a weaker assumption. [ABSTRACT FROM AUTHOR]

In this paper, we consider a faster iterative method for approximating the fixed points of generalized α -nonexpansive mappings. We prove several weak and strong convergence theorems of the considered method in mild conditions within the control parameters. In order to validate our findings, we present some nontrivial examples of the considered mappings. Furthermore, we show that the class of mappings considered is more general than some nonexpansive-type mappings. Also, we show numerically that the method studied in our article is more efficient than several existing methods. Lastly, we use our main results to approximate the solution of a delay fractional differential equation in the Caputo sense. Our results generalize and improve many well-known existing results. [ABSTRACT FROM AUTHOR]

In this paper, we consider a variational inequality problem which is defined over the intersection of the set of common fixed points of a finite family of generalized demimetric mappings and the set of common zero points of a finite family of maximal monotone mappings. We propose an iterative algorithm which combines the hybrid steepest descent method with the inertial technique to solve this variational inequality problem. Strong convergence theorem of the proposed method is established under standard and mild conditions. Moreover, we do not require any prior information regarding the Lipschitz and strongly monotone constants of the mapping. The results of this paper improve and extend several known results in the literature. [ABSTRACT FROM AUTHOR]

In this paper, we propose a novel Halpern-type algorithm and prove that the sequence generated by the algorithm converges strongly to the common element of the set of fixed points of the two firmly nonexpansive mappings and the solution set of zero points of the monotone inclusion problems on Hadamard manifolds, the main results in this paper extended and improved some recent related results. [ABSTRACT FROM AUTHOR]

The aim of this paper is to establish some common fixed point theorems for four self-mappings satisfying (E.A) and weak compatible properties and contractive type condition involving rational expressions in the setting of complex valued S-metric spaces. The results presented in this paper extend and generalize several results from the existing literature. [ABSTRACT FROM AUTHOR]

In this paper, we consider the existence and uniqueness of solutions for the following nonlinear multi-order fractional differential equation with integral boundary conditions { (C D 0 + α u) (t) + ∑ i = 1 m λ i (t) (C D 0 + α i u) (t) + ∑ j = 1 n μ j (t) (C D 0 + β j u) (t) + ∑ k = 1 p ξ k (t) (C D 0 + γ k u) (t) + ∑ l = 1 q ω l (t) (C D 0 + δ l u) (t) + σ (t) u (t) + f (t , u (t)) = 0 , t ∈ [ 0 , 1 ] , u ″ (0) = u ‴ (0) = 0 , u ′ (0) = η 1 ∫ 0 1 u (s) d s , u (1) = η 2 ∫ 0 1 u (s) d s , where 0 < δ 1 < δ 2 < ⋯ < δ q < 1 < γ 1 < γ 2 < ⋯ < γ p < 2 < β 1 < β 2 < ⋯ < β n < 3 < α 1 < α 2 < ⋯ < α m < α < 4 and η 1 + 2 (1 − η 2) ≠ 0 . Using a fixed point theorem and Banach contractive mapping principle, we obtain some existence and uniqueness results. [ABSTRACT FROM AUTHOR]

It is known that a strict contraction on a complete metric space with a graph possesses a fixed point. In the present paper, we show that this property holds for single valued and set-valued self-mappings of metric spaces with graphs that are of the contractive type. We also show the convergence of iterates of these mappings to fixed points. In particular, our results are true for metric spaces with symmetric graphs. [ABSTRACT FROM AUTHOR]

In this paper, we introduce the notion of generalized weakly contractive type multi-valued mapping with respect to a single-valued mapping and prove the existence of PPF dependent coincidence points in Banach spaces. Further, we introduce the notion of generalized weakly contractive type multivalued mappings for a pair of multi-valued mappings and prove the existence of PPF dependent common fixed points in Banach spaces. We draw some corollaries and provide nontrivial examples to illustrate our results. [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]

Type synthesis of parallel mechanism is regarded as the theoretical basis and source for the original innovation design of mechanical devices and robots. A new method for type synthesis of the fully-decoupled two-rotational and one-translational (2R1T) parallel mechanisms with three degrees of freedom is proposed in this paper. Based on the actuation wrench screw theory, the mathematical model mapping the input and output velocity vector space of the fully-decoupled 2R1T parallel mechanism is established. The actuation wrench screws and the actuated twist screws of the corresponding branches are derived according to the mathematic model. The forms of the unactuated screws are determined in terms of the reciprocal product theory. Structural synthesis of the branch chains is realized. Then type synthesis of parallel mechanisms is completed as well and lots of novel mechanisms are obtained. Finally, a 2RUPU-PU parallel mechanism synthesized is taken as an example to analyze its mobility and kinematics. Results show that the mechanism has two-rotational and one-translational degrees of freedom and its Jacobian matrix is a diagonal matrix, i.e., it has the fully-decoupled kinematic characteristics. Therefore, the method proposed is correct and effective to synthesize the fully-decoupled 2R1T parallel mechanisms. [ABSTRACT FROM AUTHOR]

This paper is devoted to studying the system of switched coupled implicit fractional Langevin equations of nonlinear form with anti‐periodic boundary conditions. In the first step, problem's equivalence and the corresponding integral equation by applying fractional calculus tools are established, and a fixed point problem is defined. For mixed monotone mappings, we have used coupled fixed point theorems to achieve the existence and uniqueness of solutions of these equations. In the next step, by using Banach's fixed point theorem, Ulam–Hyers, Ulam–Hyers–Rassias, generalized Ulam–Hyers and generalized Ulam–Hyers–Rassias stabilities of our considered model are discussed. An example is given at the end for the verification of our results. [ABSTRACT FROM AUTHOR]

In this research paper, we present a new inertial method with a self-adaptive technique for solving the split variational inclusion and fixed point problems in real Hilbert spaces. The algorithm is designed to choose the optimal choice of the inertial term at every iteration, and the stepsize is defined self-adaptively without a prior estimate of the Lipschitz constant. A convergence theorem is demonstrated to be strong even under lenient conditions and to showcase the suggested method's efficiency and precision. Some numerical tests are given. Moreover, the significance of the proposed method is demonstrated through its application to an image reconstruction issue. [ABSTRACT FROM AUTHOR]

In this paper, it is our purpose to introduce an inertial-like algorithm for approximating common fixed points of continuous pseudocontractive mappings in the framework of real Hilbert spaces. We prove strong convergence theorems for the sequence generated by the algorithm under certain conditions on the control sequences. We also provide numerical examples to demonstrate the efficiency of our algorithm. [ABSTRACT FROM AUTHOR]

In the context of uniformly convex Banach space, this paper focuses on examining the strong convergence of the F * iterative algorithm to the fixed point of a strongly pseudocontractive mapping. Furthermore, we demonstrate through numerical methods that the F * iterative algorithm converges strongly and faster than other current iterative schemes in the literature and extends to the fixed point of a strong pseudocontractive mapping. Finally, under a nonlinear quadratic Volterra integral equation, the application of our findings is shown. [ABSTRACT FROM AUTHOR]

In this paper, we first review some important definitions and notions related to best proximity point theory by considering the lack of symmetry property of quasi metric. Then, we introduce a new notion of BG-multivalued contraction mappings. Then, a best proximity point result is obtained via Q-function on quasi metric. Also, we present a noteworthy illustrative example to show the effect of our results. Finally, we give an existence and uniqueness result for the solution of nonlinear integral equations via our result. [ABSTRACT FROM AUTHOR]

In recent years fractal Weyl laws and related quantum eigenfunction hypothesis have been studied in a plethora of numerical model systems, called quantum maps. In some models studied there one can easily prove uniform hyperbolicity. Yet, a numerically sound method for computing quantum resonance states, did not exist. To address this challenge, we recently introduced a new class of quantum maps (Mertig and Shudo 2018 Phys. Rev. E 97 042216). For these quantum maps, we showed that, quantum resonance states can numerically be computed using theoretically grounded methods such as complex scaling or weak absorbing potentials (Mertig and Shudo 2018 Phys. Rev. E 97 042216). However, proving uniform hyperbolicty for this class of quantum maps was not straight forward. Going beyond that work this article generalises the class of scattering maps and provides mathematical proofs for their uniform hyperbolicity. In particular, we show that the suggested class of two-dimensional symplectic scattering maps satisfies the topological horseshoe condition and uniform hyperbolicity. In order to prove these properties, we follow the procedure developed in the paper by Devaney and Nitecki (1979 Commun. Math. Phys. 67 137–46). Specifically, uniform hyperbolicity is shown by identifying a proper region in which the non-wandering set satisfies a sufficient condition to have the so-called sector bundle or cone field. Since no quantum map is known where both a proof of uniform hyperbolicity and a methodologically sound method for numerically computing quantum resonance states exist simultaneously, the present result should be valuable to further test fractal Weyl laws and related topics such as chaotic eigenfunction hypothesis. [ABSTRACT FROM AUTHOR]

In this paper, we derive the coincidence fixed-point and common fixed-point results for ℑ-type mappings satisfying certain contractive conditions and containing fewer conditions imposed on function ℑ with regard to generalized metric spaces (in terms of Jleli Samet). Finally, a fractional boundary value problem is reduced to an equivalent Volterra integral equation, and the existence results of common solutions are obtained with the use of proved fixed-point results. [ABSTRACT FROM AUTHOR]

In this paper, we present a new type of contraction calledW-contraction in fuzzy metric space. Utilizing this contraction, we establish a unique fixed point theorem for self-map in the structure of fuzzy metric space which turns out to be generalization of fuzzy contraction given by Gregori et al. [8]. As an application of our result, we study the existence and uniqueness of the solution to nonlinear ordinary differential equations. The article also includes an example which shows the validity of our results. [ABSTRACT FROM AUTHOR]

In this paper, we construct the fixed point index for a class of contractive mapping defined by a simulation mapping and a measure of noncompact-ness noted by Zµ- contraction maps. Then we establish some fixed point theorem for this mapping of the Krasnoselskii type. An Application to the integral equation is presented to support the results. [ABSTRACT FROM AUTHOR]

In this paper, we study several classes of split inverse problems. We start with the split common fixed point problem with multiple output sets for multivalued demicontractive mappings. A relaxed inertial iterative method for solving this problem is presented and analysed. Furthermore, the method is applied to a system of split variational inequalities, system of split equilibrium problem and other related split problems. Several numerical experiments illustrate and validate the applicability of our proposed method. [ABSTRACT FROM AUTHOR]

This paper introduces a novel two-step inertial algorithm for locating a common fixed point of a countable family of nonexpansive mappings. We establish strong convergence properties of the proposed method under mild conditions and employ it to solve convex bilevel optimization problems. The method is further applied to the image recovery problem. Our numerical experiments show that the proposed method achieves faster convergence than other related methods in the literature. [ABSTRACT FROM AUTHOR]

In this paper, we first introduce the notion of neutrosophic pentagonal metric space. We prove several interesting results for some classes contraction mappings and prove some fixed point theorems in neutrosophic pentagonal metric space. Finally, we prove the uniqueness and existence of the integral equation and fractional differential equation to support our main result. [ABSTRACT FROM AUTHOR]

In this paper, we introduce the notion of graphical cone metric spaces over Banach algebra and prove some fixed point results for a particular type of contractive mappings defined on such spaces. These results extend and generalize several results from metric, graphical metric, and cone metric spaces. Some examples that demonstrate the results proved herein are provided. An application of our results to the existence of solution of a pair of initial value problems is provided. [ABSTRACT FROM AUTHOR]

In this paper, an a-complete extended Branciari b-distance space and rational α -- λ -- JS contractive conditions in the underlying spaces are introduced. Further, we establish the coincidence point, common fixed points, and uniqueness of fixed points for two pairs of mappings in new spaces under the aforementioned contractive conditions. We illustrate the work with an example and apply the results to determine the existence of solutions for a system of Urysohn integral equations. [ABSTRACT FROM AUTHOR]

In the present paper, we prove common fixed point theorems under different contractive mappings on C ★ -algebra-valued bipolar metric spaces. The results generalize and expand some well-known results from the literature. Examples and applications are given to strengthen our conclusion. Additionally, as an application of our results, we show that some classes of the nonlinear fractional differential equations with the boundary conditions have a unique common solution. [ABSTRACT FROM AUTHOR]

In this present paper, besides other things, we introduce the concept of Ćirić-generalized contractions via wt-distance and then we will prove some new fixed point results for these mappings, which generalize and improve fixed point theorems by L. B. Ćirić in [9, 8, 10] and also, B. E. Rhoades in [23]. Some examples illustrate usefulness of the new results. At the end, we will give some applications to nonlinear fractional differential equations. [ABSTRACT FROM AUTHOR]

In this paper, we introduce the concept of (g, T, G)-lower semicontinuity on mb-metric spaces and analyze the existence of points of coincidence for graph preserving hybrid pair of mappings of Feng-Liu type on such spaces. As a consequence of this study, we obtain the well-known Nadler’s fixed point theorem. Finally, we provide some examples to illustrate and justify the main result. [ABSTRACT FROM AUTHOR]

In this paper, we introduce a novel form of interpolative convex contraction and develop some new theorems by utilizing the progressive method of interpolative convex contractions. We also obtain some fixed point results for a Suzuki convex contraction in orbitally S-complete F-metric spaces. The second purpose of this research is to evaluate the effectiveness of the fixed point approach in solving fractional differential equations with boundary conditions. [ABSTRACT FROM AUTHOR]

The purpose of this paper is to prove some common fixed point theorems in S-metric spaces for a pair of self-mappings which is weakly compatible satisfying an implicit relation and give some consequences of the main result. We also give some examples to demonstrate the validity of the results and an application of the main result. The results presented in this paper generalize, extend and enrich several results in the existing literature. It specially generalize the results of Imdad et al. [10] from metric space to the setting of S-metric space. [ABSTRACT FROM AUTHOR]

One of the great ability of humans is to use mathematical formulas to replicate what they see in their daily activities, they start with simple models, when these models are unable to achieve their goals and they modify or replace them with more complex mathematical formulas. Chaos has been modelled using classical differential operators, classical with fractional orders. On the other hand, many mathematical mapping have been used to simulate some fractals behaviours. In this paper, in order to capture more fractal and chaos behaviours, we introduce the notion of chaos stochastic models and fractal stochastic mapping. We additionally present the conditions of existence and uniqueness of chaos‐stochastic models. Some numerical simulations are presented to help see the effect of stochastic functions. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

In this paper, an implicit viscosity iterative algorithm for nonexpansive mappings is proposed and investigated on Hadamard manifolds. A convergence theorem of a fixed point of a nonexpansive mapping is established on Hadamard manifolds. It is proved that the fixed point also solves a variational inequality. [ABSTRACT FROM AUTHOR]

In this paper, we study some new fixed point results in the context of w-distance as well as on wt-distance by using α-admissible mappings. Our results enhance and generalize several well known results available in the literature. We present examples to support our new findings. As an application, we utilize our results to obtain a solution of a nonlinear integral equation. [ABSTRACT FROM AUTHOR]

In this paper, we introduce the parabolic off-diagonal Muckenhoupt Ap,q+ weights. We reveal the properties of these weights, and our main results characterize them through weak-type and strong-type weighted norm inequalities for the fractional forward-in-time maximal operator. Moreover, our results cover some well-known results. [ABSTRACT FROM AUTHOR]

In this paper, we study the higher genus equivariant Gromov—Witten invariants of K ℙ 1 × ℙ 1 via Givental formalism. In particular, we prove the generating function satisfies finite generation property and holomorphic anomaly equation. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

The purpose of this paper is to extend Theorem 5 [18] to a S - metric space, without orbitally continuity, generalizing Theorem 4 [2], Theorems 1-4, 6-8 [11], Corollary 2.19 and 2.21 [23], Theorems 23, 24 [20], Theorems 3.2-3.4 [21] and to obtaining a Ćirić-Jotić-type result in S - metric spaces. [ABSTRACT FROM AUTHOR]

In this paper, some sufficient conditions for the existence of common fixed point for two mappings in the setting of C-complex valued metric space are provided. Also, common fixed point theorems for weakly compatible mappings, weakly compatible mappings along with E.A and CLR properties have been established. Furthermore, as an application of the proved result, a solution to the integral equations of Urysohns' type has been obtained. [ABSTRACT FROM AUTHOR]

In this paper, we prove some common fixed point results for two pairs of weakly compatible mappings satisfying (E:A) property and CLR-property in the framework of S-metric spaces and provide some examples to support the outcomes. We also prove well-posedness of a fixed point problem. Our findings generalize and extend a number of previously published findings. [ABSTRACT FROM AUTHOR]

In this paper, we introduce a new fuzzy contraction mapping and prove that such mappings have fixed point in τ-complete fuzzy metric spaces. As an application, we shall utilize the results obtained to show the existence and uniqueness of random solution for the following random linear random operator equation. Moreover, we shall show the existence and uniqueness of the solutions for nonlinear Volterra integral equations on a kind of particular fuzzy metric space. [ABSTRACT FROM AUTHOR]

Characterising intractable high-dimensional random variables is one of the fundamental challenges in stochastic computation. The recent surge of transport maps offers a mathematical foundation and new insights for tackling this challenge by coupling intractable random variables with tractable reference random variables. This paper generalises the functional tensor-train approximation of the inverse Rosenblatt transport recently developed by Dolgov et al. (Stat Comput 30:603–625, 2020) to a wide class of high-dimensional non-negative functions, such as unnormalised probability density functions. First, we extend the inverse Rosenblatt transform to enable the transport to general reference measures other than the uniform measure. We develop an efficient procedure to compute this transport from a squared tensor-train decomposition which preserves the monotonicity. More crucially, we integrate the proposed order-preserving functional tensor-train transport into a nested variable transformation framework inspired by the layered structure of deep neural networks. The resulting deep inverse Rosenblatt transport significantly expands the capability of tensor approximations and transport maps to random variables with complicated nonlinear interactions and concentrated density functions. We demonstrate the efficiency of the proposed approach on a range of applications in statistical learning and uncertainty quantification, including parameter estimation for dynamical systems and inverse problems constrained by partial differential equations. [ABSTRACT FROM AUTHOR]