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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]

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]

Bibliometric analysis is the quantitative study of bibliographic material. In this paper, a systematic review of papers, authors, and journals is carried out. This is necessary to determine and set targets to be achieved in further research. The main objective of this study is to identify some of the most relevant research and the latest trends according to the information found in the Google Scholar, Publish or Perish, Science Direct, and Dimension databases. The methods used are classification, analysis of the most cited journals of all time, and the most prolific and influential authors. The results are information on the number of papers, citations, researchers, h-index, g-index, major reference journals, and visualization of research roadmaps for the topic of agricultural insurance mathematical models. The research findings identify the core themes, which are used as research gaps for future research. [ABSTRACT FROM AUTHOR]

This paper illustrates the use of curriculum mapping as a process that can support productive boundary encounters between lecturers in an initial teacher education (ITE) programme as part of curriculum review. Using mathematics as the context, lecturers in a 1-year primary graduate ITE programme developed a curriculum map to identify the mathematical thinking opportunities available to their pre-service teachers in their courses and across the programme. The coordinated approach to curriculum analysis/mapping expanded lecturers' definition of mathematical skills and reasoning and their awareness of opportunities their students had to engage with mathematical ideas. The mapping process included collaborative discussions, document analysis and iterative development of a curriculum map. In an overcrowded curriculum, which responds to government policies and university initiatives such as embedding critical literacy, mathematical foundations and cross-disciplinary study, the mapping process has potential to meet multiple demands and agendas. In our study, the mapping process and the map offered purposeful and productive grounds for learning and development. They were central to facilitating dialogic boundary encounters between programme lecturers resulting in the re-conceptualisation of course and programme curriculum boundaries. We expect study findings will be of interest to programme leaders, lecturers and researchers facing the challenge of identifying and supporting the development of competencies and multi-literacies that span courses and programmes. [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]

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]

In this paper, we introduce a regularized iterative scheme for solving the split common fixed point problem of asymptotically demicontractive and demimetric mappings in real Banach spaces. We then prove that the iterative scheme converges strongly to a solution to the problem, which is also a solution to a variational inequality problem. A split feasibility problem is also considered with the aid of our scheme. [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]

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]

Slovakia has many world-class mathematicians who can be an inspiration for the younger generation. The aim of this paper is to present the results of the project, which captures important Slovak mathematicians and maps important mathematical workplaces in Slovakia. The paper will focus on one of the last processed personalities of mathematics at prof. Ján Čižmar. [ABSTRACT FROM AUTHOR]

Achieving scientific document retrieval by considering the wealth of mathematical expressions and the semantic text they contain has become an inescapable trend. Current scientific document matching models focus solely on the textual features of expressions and frequently encounter hurdles like proliferative parameters and sluggish reasoning speeds in the pursuit of improved performance. To solve this problem, this paper proposes a scientific document retrieval method founded upon hesitant fuzzy sets (HFS) and local semantic distillation (LSD). Concretely, in order to extract both spatial and semantic features for each symbol within a mathematical expression, this paper introduces an expression analysis module that leverages HFS to establish feature indices. Secondly, to enhance contextual semantic alignment, the method of knowledge distillation is employed to refine the pretrained language model and establish a twin network for semantic matching. Lastly, by amalgamating mathematical expressions with contextual semantic features, the retrieval results can be made more efficient and rational. Experiments were implemented on the NTCIR dataset and the expanded Chinese dataset. The average MAP for mathematical expression retrieval results was 83.0%, and the average nDCG for sorting scientific documents was 85.8%. [ABSTRACT FROM AUTHOR]

Requirements engineering (RE) has attracted a great deal of attention from researchers and practitioners in recent years. Requirements engineering education (REE) is therefore an important undertaking if the field is to have professionals who are capable of successfully accomplishing software projects. This increasing interest demands that academia should provide software engineering students with a solid foundation in the subject matter. This paper aims to identify and to present the current research on REE that is available at present, and to select useful approaches and needs for future research. A systematic mapping study was therefore performed to classify the selected studies into five classification criteria: research type, empirical type, contribution type, RE activity, and curricula. A total of 79 papers were selected and classified according to these criteria. The results of this systematic mapping study are discussed, and a list of advice obtained from the REE literature for instructors is provided. [ABSTRACT FROM AUTHOR]

This paper presents the stability theorem for the T-Picard iteration scheme and establishes the existence and uniqueness theorem for fixed points concerning T-mean nonexpansive mappings within b-metric-like spaces. The outcome of our fixed point theorem substantiated the existence and uniqueness of solutions to the Fredholm-Hammerstein integral equations defined on time scales. Additionally, we provided two numerical examples from distinct time scales to support our findings empirically. [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]

This article is devoted to the study of mappings with bounded and finite distortion defined in some domain of the Euclidean space. We consider mappings that satisfy some upper estimates for the distortion of the modulus of families of paths, where the order of the modulus equals to p, n - 1 < p ⩽ n. The main problem studied in the manuscript is the investigation of the boundary behavior of such mappings, more precisely, the distortion of the distance under mappings near boundary points. The publication is primarily devoted to definition domains with "bad boundaries", in which the mappings not even have a continuous extension to the boundary in the Euclidean sense. However, we introduce the concept of a quasiconformal regular domain in which the specified continuous extension is valid and the corresponding distance distortion estimates are satisfied; however, both must be understood in the sense of the socalled prime ends. More precisely, such estimates hold in the case when the mapping acts from a quasiconformal regular domain to an Ahlfors regular domain with the Poincar'e inequality. The consideration of domains that are Ahlfors regular and satisfy the Poincar'e inequality is due to the fact that, lower estimates for the modulus of families of paths through the diameter of the corresponding sets hold in these domains. (There are the so-called Loewner-type estimates). We consider homeomorphisms and mappings with branching separately. The main analytical condition under which the results of the paper were obtained is the finiteness of the integral averages of some majorant involved in the defining modulus inequality under infinitesimal balls. This condition includes the situation of quasiconformal and quasiregular mappings, because for them the specified majorant is itself bounded in a definition domain. Also, the results of the article are valid for more general classes for which Poletsky-type upper moduli inequalities are satisfied, for example, for mappings with finite length distortion. [ABSTRACT FROM AUTHOR]

This paper introduces the innovative concept of (τ, α)-weak contractive mappings. We establish several fixed point results without relying on conditions essential in prior works. Examples are presented to showcase our key findings, particularly in scenarios where earlier research outcomes are not applicable. Furthermore, we provide an application of our obtained results to fractional differential equations involving non-singular and non-local kernels. [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 first introduce the notion of (incident) higher-order generalized epiderivative for a set-valued map and obtain a crucial result of the epiderivative. Then we use this result to establish the higher-order sufficient and necessary optimality conditions of a constrained set-valued optimization problem. By virtue of the epiderivatives and the optimality conditions, we establish the higher-order mixed duality problem for the set-valued optimization problem and obtain the corresponding duality theorems. [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]

This paper delves into an inquiry that centers on the exploration of fractional adaptations of Milne-type inequalities by employing the framework of twice-differentiable convex mappings. Leveraging the fundamental tenets of convexity, Hölder's inequality, and the power-mean inequality, a series of novel inequalities are deduced. These newly acquired inequalities are fortified through insightful illustrative examples, bolstered by rigorous proofs. Furthermore, to lend visual validation, graphical representations are meticulously crafted for the showcased examples. [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]

In this paper, first the congruences in the category PosAct-S of all poset acts over a pomonoid S; an S-act in the category Pos of all posets, with action preserving monotone maps between them, are introduced. Then, we study the existence of the free and cofree objects in the category PosAct-S. More precisely, we consider all forgetful functors between this category and the categories Pos-S of all S-posets, Pos of all posets, Act-S of all S-acts, and Set of all sets, and we study the existence of their left and right adjoints. It is shown that the category Pos-S is a full reflective and coreflective subcategory of PosAct-S. [ABSTRACT FROM AUTHOR]

In the paper we study equiaffine immersions f: (Mn,∇) → Rn+2 with flat connection ∇ and one-dimensional Weingarten mapping. For such immersions there are two types of the transversal distribution equiaffine frame. We give a parametrization of a submanifold with the given properties for both types of equiaffine frame. The main result of the paper is contained in Theorems 1, 2 and Corollary 1: Let f: (Mn,∇) → (Rn+2,D) be an affine immersion with pointwise codimension 2, equiaffine structure, flat connection ∇, one-dimensional Weingarten mapping then there exists three types of its parametrization: (i)→r = g(u¹, . . ., un)→a1 + R→φ(u¹)du¹ + nΣi=2 ui→ai; (ii)→r = (g(u², . . ., un) + u¹)→a + ∫v(u¹)→η(u1)du¹ + Σni=2 ui ∫ λi(u¹)→η(u¹)du¹; (iii)→r = (g(u², . . ., un) + u¹)→ρ(u¹) + ∫ (v(u¹) - u¹) d→ρ(u¹)/du¹du¹ + Σni=2 ui ∫ λi(u¹) d→ρ(u¹). du¹du1. [ABSTRACT FROM AUTHOR]

Big data (BD) is one of the emerging topics in the field of information systems. This article utilized citation and co-citation analysis to explore research articles in the field of BD to examine the scientific development in the area. The research data was retrieved from the WOS database from the period between 2005 and June 2016, which consists of 366 articles. In the citation analysis, this article relies on the degree centrality and betweenness centrality for identifying 38 important papers in BD. In the co-citation analysis, a principal component factor analysis of the co-citation matrix is employed for identifying six major research themes: foundations, BD applications, techniques and technologies, challenges, adoption and impacts and literature review. This literature review is one of the first studies to examine the knowledge structure of BD research in the information systems discipline by using evidence-based analysis methods. Recommendations for future research directions in BD are provided based on the analysis and results of this study. [ABSTRACT FROM AUTHOR]

This paper studies λ-constacyclic codes and skew λ-constacyclic codes over the finite commutative non-chain ring R = Z4 + uZ4 + u²Z4 with u3 = 0 for λ = (1 + 2u + 2u²) and (3 + 2u + 2u²). We introduce distinct Gray maps and show that the Gray images of λ-constacyclic codes are cyclic, quasi-cyclic, and permutation equivalent to quasi-cyclic codes over Z4. It is also shown that the Gray images of skew λ-constacyclic codes are quasi-cyclic codes of length 2n and index 2 over Z4. Moreover, the structure of λ-constacyclic codes of odd length n over the ring R is determined and give some suitable examples. [ABSTRACT FROM AUTHOR]

The main aim of our manuscript is to present common fixed point solution for Urysohn integral equation 41, Our paper divided in to two folds, Firstly with the help of class function we established fixed point results for two pair of weakly compatible mapping satisfying the contractive condition of rational type in CVMS our work inspired from [15]. Secondly Common solution to the integral equation, .... [ABSTRACT FROM AUTHOR]

In this paper, we introduce triple θ-centralizers and weak triple θ-centralizers on an algebra A, where θ: A → A is a triple homomorphism. Some observations concerning triple θ-centralizers, weak triple θ-centralizers and approximate weak triple θ-centralizers are given. [ABSTRACT FROM AUTHOR]

In this paper, we consider some numerical aspects of branched continued fractions as special families of functions to represent and expand analytical functions of several complex variables, including generalizations of hypergeometric functions. The backward recurrence algorithm is one of the basic tools of computation approximants of branched continued fractions. Like most recursive processes, it is susceptible to error growth. Each cycle of the recursive process not only generates its own rounding errors but also inherits the rounding errors committed in all the previous cycles. On the other hand, in general, branched continued fractions are a non-linear object of study (the sum of two fractional-linear mappings is not always a fractional-linear mapping). In this work, we are dealing with a confluent branched continued fraction, which is a continued fraction in its form. The essential difference here is that the approximants of the continued fraction are the so-called figure approximants of the branched continued fraction. An estimate of the relative rounding error, produced by the backward recurrence algorithm in calculating an nth approximant of the branched continued fraction expansion of Horn's hypergeometric function H4, is established. The derivation uses the methods of the theory of branched continued fractions, which are essential in developing convergence criteria. The numerical examples illustrate the numerical stability of the backward recurrence algorithm. [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]

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, to introduce approximate efficiency notions in variable ordering structures, some coradiant-valued maps are dealt with. Approximate nondominated and minimal elements are defined and some of their properties are studied. Corresponding to these concepts, necessary and sufficient conditions are provided. To obtain such conditions, some scalarization methods are investigated. The paper also investigates possible relationships between the Pascoletti-Serafini radial scalarization, approximate efficiency, approximate nondominance, and minimality utilizing some coradiant-valued maps. [ABSTRACT FROM AUTHOR]

When taking images in low light conditions, images often suffer from low visibility. In addition to affecting the sensory quality of images, this poor quality may also significantly limit the performance of various computer vision systems. Many grey-level mapping enhancement algorithms based on classic mapping functions, such as the gamma mapping function, have been proposed in recent years to improve the visual quality of low-light images. However, the classic mapping function cannot coordinate the greyscale distribution of the bright and dark areas of the image well and may easily lead to excessive enhancement. This makes it difficult for the performance of these improved algorithms to be fully utilized. Therefore, this paper proposes a new multiparameter grey mapping method. Unlike the classic mapping function, the new mapping method is based on the enhancement strategy of compressing the bright area and then adjusting the dark area. Thus, the inherent shortcomings of the classic mapping function are fundamentally overcome. The new mapping method can not only directly control the compression of the grey space in the bright area of the image through parameters, but it can also adjust the greyscale distribution of dark areas without changing the greyscale value of the pixels in the bright area. Finally, this paper also designs an adaptive enhancement algorithm with the new mapping method as the core to verify its effectiveness and flexibility. Experimental results showed that the adaptive algorithm had excellent performance in colour rendering, brightness enhancement and noise suppression. It was also obviously better than the current similar algorithms in visual quality and quantitative tests. [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]

The purpose of this paper is to prove some common fixed point theorems for two pairs of self-mappings satisfying (CLR)-property and some Φ-type contractive condition in the framework of S-metric spaces. We also give some examples to validate the results. The results presented in this paper generalize, extend and unify several previous results in the existing literature. [ABSTRACT FROM AUTHOR]

In this paper, we consider differential systems of the following structure: at two consecutive time intervals the motion of the object is described by two different systems of differential equations. We study the controllability of the object described by such system from the initial set in one space to the given set in another space through so-called "transition hypersurface". The transition of an object from one space to another one is given by a certain reflection. Sufficient conditions of the controllability of such differential systems in the problem with phase space change are obtained. Approaches to the study of both nonlinear and linear systems are considered. [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 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 the paper, nonlinear vibration characteristics of a rotor system are investigated. Such a nonlinear rotor system is subjected to brush seal forces, which are obtained by integrating the bristle force along the entire ring. The nonlinear brush seal rotor system is constructed by merging a flexible rotor with nonlinear seal forces. The research is aimed at studying the nonlinear vibration characteristics and bifurcations of the motions under a variety of eccentricity circumstances. Different kinds of bifurcations are successfully obtained by mathematical discretization and mapping manipulation. Such a discrete mapping method successfully predicts the stable and unstable motions accurately. The period-doubling bifurcations and saddle node bifurcations of the rotor system are obtained. The sole unstable solutions are obtained, which are special, and a normal numerical integration method cannot solve this problem, which provides advantages in rotor design and motion control. According to the results, nonlinear resonances are found between the stable and unstable motions. The greater the eccentricity of the rotor, the greater the number of bifurcation points that occur during the rotor's nonlinear motions, as well as the larger the ranges of speeds where the motions are unstable. Saddle node bifurcations generate unstable nonlinear motions and non-smooth motions, which may bring damage to the mechanical rotors. The period-doubling bifurcations produce the route from period-1 to period-2 motions in the nonlinear rotor system. The research provides a new perspective to study the bifurcations and stability of the nonlinear rotor systems. [ABSTRACT FROM AUTHOR]

In this paper, we introduce a new hybrid relaxed iterative algorithm with two half-spaces to solve the fixed-point problem and split-feasibility problem involving demicontractive mappings. The strong convergence of the iterative sequence produced by our algorithm is proved under certain weak conditions. We give several numerical experiments to demonstrate the efficiency of the proposed iterative method in comparison with previous algorithms. [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]

The purpose of this paper is to establish a common fixed point result in Menger space in two pairs and three pairs of self mappings by using occasionally weakly compatible mappings. Our first theorem generalizes the theorem of Sharma and Shahu [1] and B. Fisher et al. [2] and both theorems deduce some similar results in the literature. [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]

This paper aims to establish some results on the structure of fixed point sets for mappings in 2-inner product spaces. To this end, we employ some well-known techniques of 2-inner product spaces. [ABSTRACT FROM AUTHOR]

This work focuses on quasi efficient solutions of a vector optimization problem. Namely, it is assumed the objective function to map values between finite dimensional spaces and the ordering in the final space is defined by a pointed convex cone. In this setting, several new concepts of quasi efficient solutions are introduced and their basic properties are obtained. After that, it is studied their limit behavior in order to deduce when they approximate well other kind of efficient solutions of the problem. Finally, in convex problems, linear scalarization results are stated that relate the introduced quasi efficient solutions with solutions of scalar optimization problems. The concepts and results of the paper extend and clarify several ones of the recent literature. [ABSTRACT FROM AUTHOR]