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Two of the most well-known belief contraction operators are partial meet contractions (PMCs) and kernel contractions (KCs). In this paper we propose two new classes of contraction operators, namely the class of generalized partial meet contractions (GPMC) and the class of generalized kernel contractions (GKC), which strictly contain the classes of PMCs and of KCs, respectively. We identify some extra conditions that can be added to the definitions of GPMCs and of GKCs, which give rise to some interesting subclasses of those classes of functions, namely the classes of extensional and of uniform GPMCs/GKCs. In the context of contractions on belief sets the classes of partial meet contractions, uniform GPMCs and extensional GPMCs are all identical. Nevertheless, when considered as operations on belief bases, the class of uniform GPMCs coincides with the class of partial meet contractions, but the extensional GPMCs constitute a new kind of belief base contraction functions whose characterizing postulate of irrelevance of syntax is extensionality—the same postulate of irrelevance of syntax which occurs in the classical axiomatic characterization of partial meet contractions for belief sets—rather than the postulate of uniformity—which is the irrelevance of syntax postulate used in the axiomatic characterization for partial meet contractions on belief bases. Analogous results are obtained regarding the classes of extensional and of uniform GKCs. We present the interrelations in the sense of inclusion among all the new classes of operators presented in this paper and several well known classes of PMCs and of KCs. [ABSTRACT FROM AUTHOR]

The purpose of this paper is to introduce a novel fixed point iterative scheme based on Green's function, called the Picard–Ishikawa–Green's iterative scheme and use it in approximating the solution of boundary value problems (BVPs). It is proved that Picard–Ishikawa–Green's scheme converges strongly for an integral operator which represents the solution of BVP and the scheme is stable. Moreover, we prove that the integral operator is a contraction. Furthermore, it is shown that the novel scheme converges faster than all of Ishikawa–Green's, Khan–Green's, and Mann–Green's schemes. Finally, numerical examples are given to substantiate the validity of our results for third‐order BVPs. Our results extend and generalize several other results in literature. [ABSTRACT FROM AUTHOR]

In this paper, we study a type of nonlinear hybrid Δ-difference equations of fractional-order. The main objective is to establish some stability criteria including the Ulam–Hyers stability, generalized Ulam–Hyers stability together with the Mittag-Leffler–Ulam–Hyers stability for the addressed problem. Prior to the stabilization processes, solvability criteria for the existence and uniqueness of solutions are considered. For this purpose, a hybrid fixed point theorem for triple operators and the Banach contraction mapping principle are applied, respectively. For the sake of illustrating the practical impact of the proposed theoretical criteria, we finish the paper with particular examples. [ABSTRACT FROM AUTHOR]

In this paper, we are concerned with the optimal integrability, regularity and symmetry of integrable solutions for the following Wolff type integral systems: (1.1) { u (x) = R 1 (x) W β , γ (v q) (x) , u (x) > 0 , x ∈ R N , v (x) = R 2 (x) W β , γ (u p) (x) , v (x) > 0 , x ∈ R N , where γ > 2 , β > 0 , β γ < N , p , q > γ − 1 with γ − 1 p + γ − 1 + γ − 1 q + γ − 1 = N − β γ N , R 1 , R 2 are double bounded in R N and W β , γ (h) (x) : = ∫ 0 ∞ [ ∫ B t (x) h (y) d y t N − β γ ] 1 γ − 1 d t t. Firstly, we prove the optimal integrability and boundedness of solutions (u , v) ∈ L p + γ − 1 (R N) × L q + γ − 1 (R N) for system (1.1) , by constructing a nonlinear, contracting operator and applying the regularity lifting lemma of C. Ma, W. Chen and C. Li (2011) [21]. Moreover, we exploit the general regularity lifting theorem to derive the Lipschitz continuity of u and v when R 1 ≡ R 2 ≡ 1 in R N. These extend the above important results of C. Ma, W. Chen and C. Li to γ > 2. We also prove that u and v vanish at infinity. As the corollaries of the above results, we obtain the optimal integrability, boundedness and the property of vanishing at infinity of integrable solutions for the corresponding γ -Laplace and k -Hessian systems. Secondly, we use the method of moving planes in integral forms to prove the symmetry and monotonicity of solutions (u , v) ∈ L p + γ − 1 (R N) × L q + γ − 1 (R N) for system (1.1) when R 1 ≡ R 2 ≡ 1 in R N , which extends the useful result of W. Chen and C. Li (2011) [5] to γ > 2. In comparison with the above two papers, Minkowski's inequality is crucial in our proofs. We believe that our arguments can be used to prove similar results for other Wolff type integral systems when γ > 2. [ABSTRACT FROM AUTHOR]

In this paper, we introduce a new mapping namely L-contraction for fixed function and we also prove a novel fixed function theorem using L-contraction mapping. Moreover, we apply our result to solve integral equation. [ABSTRACT FROM AUTHOR]

The bounded linear operators T on a Hilbert space which have 2-isometric liftings S on are investigated in this paper. We refer to the structure of those operators in the case of general liftings, as well as for a more special type of such liftings S, namely for which is invariant to the orthogonal projection onto the kernel of S∗S − I. In this special case we describe the canonical triangulation of T induced by S, with entries expressed by operators close to contractions or isometries. Also, in this case we refer to some asymptotic properties of T and of its adjoint T∗ obtained by means of asymptotic limits associated to T∗ and T, relative to a lifting S for T. The canonical triangulations of T in this setting are described in detail, and as an application, the Wold type decomposition of a concave operator is obtained. [ABSTRACT FROM AUTHOR]

Nowadays, the issue of traffic flow assignment has become an interdisciplinary topic that concerns multiple research areas and branches of science. This work is focussed on the mathematical and computational aspects of the equilibrium traffic assignment problem in the case when route flows are considered to be decision variables. Firstly, we obtain a fixed-point mapping with the explicit contraction operator, which is proven to equilibrate the journey times on feasible routes between a single origin-destination pair of nodes with the quadratic rate. Remarkable that from mathematical perspectives, the developed operator generalizes most path-equilibration operators already exploited by researchers. Secondly, we use the obtained fixed-point procedure to run the sequential path-equilibration algorithm for traffic flow assignment on well-known test urban road networks with arc-additive travel time functions. Our computational results appear to demonstrate higher accuracy of user-equilibrium traffic assignment solutions than the best ones known to us. In other words, developed within this paper sequential path-equilibration algorithm leads to solutions with less goal function values compared to the best solutions for today, according to our knowledge. [ABSTRACT FROM AUTHOR]

In the present paper, we introduce a new three-step fixed point iteration called SNIA-iteration (Naveen et al. iteration) which converges faster than the original iteration. It is possible by introducing a contraction operator on the existing iteration algorithm where the coefficients of the new iterative process are chosen in (1 2 , 1) instead of [0, 1]. The strong convergence result for the SNIA-iteration method is also proved by showing the convergence of this iteration method towards its fixed point. Further, the coefficients involved in SNIA-iteration have been interchanged, and then the result is compared with the original iteration. It is found that the new result is better than the previous one in the sense of its rate of convergence for contraction mappings. [ABSTRACT FROM AUTHOR]

This paper proves a new q-Hermite-Hadamard inequality for convex functions using quantum integrals. We also prove some new midpoint-type inequalities for q-differentiable convex functions. Moreover, we present some examples to illustrate our established results, supplemented with graphs. [ABSTRACT FROM AUTHOR]

In this paper, some sufficient conditions for the oscillation of all solutions of second order dynamic equations with a negative sub-linear neutral term are established. The obtained results provide a unified platform that adequately covers both discrete and continuous equations. Furthermore, it covers a wide range of equations by utilizing different time scales. Illustrative examples are provided. [ABSTRACT FROM AUTHOR]

In this research paper, we investigate some new identifies for Sarıkaya fractional integrals which introduced by Sarıkaya and Ertugral in [20]. The fractional integral operators also have been applied to Hermite-Hadamard type integral inequalities to provide their generalized properties. Furthermore, as special cases of our main results, we present several known inequalities such as Simpson, Bullen, trapezoid for convex functions. [ABSTRACT FROM AUTHOR]

In this paper, we are concerned with the following integral system u i (x) = ∫ ℝ n u i + 1 p i + 1 (y) | x − y | n − α d y , i = 1 , 2 , ... , m − 1 , u m (x) = ∫ ℝ n u 1 p 1 (y) | x − y | n − α d y , m ≥ 1 , n ≥ 1 , where u i > 0 , 0 < α < n , and p i > 1 (i = 1 , 2 , ... , m). When m ∈ { 1 , 2 } , such an integral system is associated with the best constants of the Hardy–Littlewood–Sobolev inequality. Chen, Li and their cooperators obtained optimal integrability intervals of the finite energy solutions by an argument of contraction and shrinking operators. This result is helpful to well understand the classification of the extremal functions of the Hardy–Littlewood–Sobolev inequality. The critical condition plays a key role in their work. In this paper, we study optimal integrability intervals when the positive solutions have some initial integrability. Now, the critical condition is not necessary, and we apply a weaker condition, the Serrin-type condition, to establish some important relations of exponents which come into play to lift the regularity. In addition, we also generalize this result to the case of m ∈ ℤ + . [ABSTRACT FROM AUTHOR]

Telecommunications companies are constantly chasing continuous technological advances with their management methods of Operations & Maintenance (O&M) that still struggle to turn their eye toward innovation and simplification of processes. In a future that aims at fully fiber-optic networks, the objective of the research is to propose guidelines and provide data to support the Wholesale Operator for the definition of the acceptable attenuation threshold on the Passive Optical Network Fiber-To-The-Home (PON FTTH) infrastructure to determine the Service Level Agreements (SLA) to be contracted with Retail Operators. Following exceeding the threshold, the Retail Operator has the right to open a Trouble Ticket to request the resolution of the anomaly. Consequently, the definition of the attenuation threshold strongly affects the number of Trouble Tickets to be managed and the related costs the Wholesale Operator bears. This paper analyzes a specific case of the PON FTTH network of the Italian wholesale operator Open Fiber. The studied infrastructure, with a length of 11 km, allows a maximum attenuation of 37 dB without degrading the service. An economic model has been proposed to assess the cost impact of moving the attenuation threshold in the SLA. [ABSTRACT FROM AUTHOR]

In this paper we investigate the existence of a solution of Integral equations of fractional order via Hadamard's fractional integral by reducing the research to the search of the existence of fixed points of appropriate operators. The nonlinear alternative fixed point theorem for the sum of a completely continuous operator and a contraction one in Frechet spaces due to Avraniescu and a fractional version of Pachpatte's inequality are the main tools in this study. We demonstrate the existence of a solution with a suitable illustrative example. [ABSTRACT FROM AUTHOR]

In open quantum systems, the quantum Zeno effect consists in frequent applications of a given quantum operation, e.g., a measurement, used to restrict the time evolution (due, for example, to decoherence) to states that are invariant under the quantum operation. In an abstract setting, the Zeno sequence is an alternating concatenation of a contraction operator (quantum operation) and a C 0 -contraction semigroup (time evolution) on a Banach space. In this paper, we prove the optimal convergence rate O (1 n) of the Zeno sequence by proving explicit error bounds. For that, we derive a new Chernoff-type n -Lemma, which we believe to be of independent interest. Moreover, we generalize the convergence result for the Zeno effect in two directions: We weaken the assumptions on the generator, inducing the Zeno dynamics generated by an unbounded generator, and we improve the convergence to the uniform topology. Finally, we provide a large class of examples arising from our assumptions. [ABSTRACT FROM AUTHOR]

In this paper, we investigate an orthogonal L ⋆ -contraction map concept and prove the fixed-point theorem in an orthogonal complete Branciari metric space (OCBMS). We also provide illustrative examples to support our theorems. We demonstrated the existence of a uniqueness solution to the fourth-order differential equation using a more orthogonal L ⋆ contraction operator in OCBMS as an application of the main results. [ABSTRACT FROM AUTHOR]

Discussions of the issue of iterated belief revision are commonly accompanied by the presentation of three "concrete" operators: natural, restrained and lexicographic. This raises a natural question: What is so distinctive about these three particular methods? Indeed, the common axiomatic ground for work on iterated revision, the AGM and Darwiche-Pearl postulates, leaves open a whole range of alternative proposals. In this paper, we show that it is satisfaction of an additional principle of "Independence of Irrelevant Alternatives", inspired by the literature on Social Choice, that unites and sets apart our three "elementary" revision operators. A parallel treatment of iterated belief contraction is also given, yielding a family of elementary contraction operators that includes, besides the well-known "conservative" and "moderate" operators, a new contraction operator that is related to restrained revision. [ABSTRACT FROM AUTHOR]

This paper introduces a new iteration process for the approximation of fixed points of contraction mapping. We prove the comparison theorem to indicate that our iteration process converges faster than the other iteration processes and also prove data dependence, stability. and convergence results. Moreover, we give numerical examples to check the performance of our algorithm over the Piri, SM, CR, and K* iterations process for different types of functions. [ABSTRACT FROM AUTHOR]

In this paper we investigate AGM belief contraction operators by using the tools of algebraic logic. We generalize the notion of contraction to arbitrary finitary propositional logics, and we show how to switch from a syntactic-based approach to a semantic one. This allows to build a solid bridge between the validity of AGM postulates in a propositional logic and specific algebraic properties of its intended algebraic counterpart. Such a connection deserves particular attention when we deal with maxichoice contractions, as studied in the final part of the paper. [ABSTRACT FROM AUTHOR]

As an important emission reduction source for the transportation industry, biofuel has received strong support from the Chinese government. However, the development of the biofuel industry is still struggling. The high degree of uncertainty makes the development of the industry face huge challenges. Kitchen waste, as a biodiesel raw material with a large yield, has good development prospects. Reuse of kitchen waste can solve public health and safety problems. This paper proposes a two-stage stochastic programming model under supply disturbance to optimize the supply chain from the perspective of contract. Then current three main flow directions of kitchen waste are analysed and the reasonable price for biodiesel operators to purchase is determined. By signing contracts with the biodiesel operators, restaurant is guaranteed and encouraged to provide a certain percentage of kitchen waste to meet the demand for biodiesel production. Using actual case in the Yangtze River Delta region, the performance of the stochastic programming model under disturbance was compared. Through the sensitivity analysis of different parameters, this paper determines the influence of its supply chain network design and expected total system cost. Through the optimization of the waste cooking oil (WCO) for biodiesel supply chain, this paper can effectively improve the efficiency of the supply chain, reduce system costs, increase the profits of biofuel operators, and promote the sustainable development of the biofuel industry. [ABSTRACT FROM AUTHOR]

The unique solvability of the inverse problem of recovering the source function in a nonuniformly parabolic equation with many independent variables in a bounded domain is proved. As an additional condition, the integral observation condition is given. The unknown source function can be found by iteration from the operator equation with contraction operator. An example of an the inverse problem for which the results proved in this paper are applicable is presented. The results obtained for the inverse problem are based on the preliminary study of the unique solvability of the corresponding direct problem, which is also of interest in itself. [ABSTRACT FROM AUTHOR]

The aim of this paper is to present a common fixed point theory for a pair of multivalued operators in complete metric spaces. Existence and stability results for the common fixed point problem will be discussed. The approach is based on some fixed point results for multivalued graphical contractions and for multivalued operators of Feng-Liu type. Our results extend to the multivalued case some recent results in the literature. [ABSTRACT FROM AUTHOR]

An efficient solution of the three-dimensional Helmholtz equation is known to be crucial in many applications, especially geophysics. In this paper, we present and test two preconditioning approaches for the discrete problem resulting from the second order finite-difference discretization of this equation. The first approach combines shifted-Laplacian preconditioner with inversion of a separable matrix, corresponding to the horizontally-layered velocity model, using fast Fourier based transforms. The second approach is novel and involves a special transformation resulting in a preconditioner with a contraction operator (CO preconditioner). The two approaches have near the same arithmetical complexity; however, the second approach, developed in this paper, provides a faster convergence of an iterative solver as illustrated by numerical experiments and analysis of the spectral properties of the preconditioned matrices. Our numerical experiments involve parallel modeling of highly heterogeneous lossy and lossless media at different frequencies. We show that the CO-based solver can tackle problems with hundreds of millions of unknowns on a conventional cluster node. The CO preconditioned solver demonstrates a very moderate increase of iteration count with the frequency. We have conducted a comparison of the performance of the developed method versus open-source parallel sweeping preconditioner. The results indicate that, the CO solver is several times faster with respect to the wall-clock time and consumes substantially less memory than the code based on the sweeping preconditioner at least in the example we tested. [ABSTRACT FROM AUTHOR]

• The paper examines how transit authorities may influence traffic safety through requirements set in the contracts with bus companies. • Transit authorities may have direct influence on traffic safety, especially if they set requirements that exceeds (inter) national legislation. • Indirect impact on traffic safety through contracts is related to requirements for punctuality and regularity, which we find to be related to drivers' stress, driving style and accident involvement. • Environmental concerns also influence traffic safety indirectly, as it influences the use of large buses in narrow streets, to maintain and increase a high passenger capacity. The main objective of the study is to evaluate direct and indirect traffic safety consequences of the requirements that Norway's largest transit authority (Ruter) sets in the contracts with bus companies. To assess the representativity of Ruter's requirements and its consequences, the data focuses both on Ruter and transit authorities from other areas in Norway, serving a mix of urban and rural areas. The study is based on qualitative interviews (N = 18), a workshop, reviews of documents and a quantitative survey (N = 1012). The study indicates that transit authorities may have direct influence on traffic safety, especially if they set requirements that exceeds (inter) national legislation. Ruter does that when it comes to driver collision protection and blind zone warning systems. We also find indications of indirect impact on traffic safety through the contracts. This is firstly related to the requirements for punctuality and regularity, which we find to be related to drivers' stress, driving style and accident involvement in our quantitative analysis. It is secondly related to environmental concerns, which motivate maintaining (and increasing) a high level of passengers. Interviewees said that this influences the types of buses specified in contracts (e.g. large high capacity buses), and their routes (e.g. in narrow streets, "where people live"). They also emphasized that roads and infrastructure, for example in Oslo, are poorly adapted to bus transport. In our quantitative analysis, we found that buses that are poorly adapted to the roads they are used on, and roads that are poorly adapted to bus transport were related to bus drivers' reported stress and time pressure, which were related to risky driving style, which in turn was related to accidents. Based on the study, we developed several policy implications, that we believe also can be relevant for, and inspire other transit authorities. Ruter has applied several of these changes after our study (e.g. requiring ISO:39001 certification from the bus operators in the contracts, starting to develop a system to learn from accidents), and may thus stand out as a transit authority that other may learn from when it comes to management of traffic safety. [ABSTRACT FROM AUTHOR]

A newly developed method in the mixed space–wavenumber domain is proposed for 3D DC resistivity modeling in anisotropic structures. Unlike the traditional method for numerical simulation of DC resistivity, this method performs a 2D Fourier transform directly on the partial differential equation of DC abnormal potential along the horizontal direction, so that the horizontal direction is converted into the wavenumber domain while the vertical direction remains in the spatial domain. In this way, the 3D partial differential equation in the spatial domain is transformed into a 1D ordinary differential equation in different wave numbers. Therefore, a large-scale 3D numerical simulation problem is decomposed into many 1D numerical simulation problems. The 1D finite element method is used to solve the equations, and a contraction operator is used for iterative calculation to obtain a highly accurate solution. The accuracy of the algorithm is verified by comparison with the goal-oriented adaptive finite element method. Compared with the COMSOL Multiphysics commercial finite element simulation software, the algorithm in this paper has high computational efficiency. To identify the electrical anisotropy, we propose a new measurement and then use it to study the response characteristics of a half-space model with two prisms. The test results show that this measurement can accurately reflect the underground electrical anisotropy. Finally, the code is applied to the numerical simulation of a vertical-borehole survey and shows that the significant information on the hydraulically induced fracturing system can be reflected well by the electric anisotropy. [ABSTRACT FROM AUTHOR]

The purpose of this paper is to introduce the class of enriched interpolative Kannan type operators on Banach space that contains the classes of enriched Kannan operators, interpolative Kannan type contraction operators and some other classes of nonlinear operators. Some examples are presented to support the concepts introduced herein. A convergence theorem for the Krasnoselskii iteration method to approximate fixed point of the enriched interpolative Kannan type operators is proved. We study well-posedness, Ulam-Hyers stability and periodic point property of operators introduced herein. As an application of the main result, variational inequality problem is solved. [ABSTRACT FROM AUTHOR]

The aim of this paper is to improve some fixed point results given by I.A. Rus in (On a fixed point theorem of Maia, Studia Univ. Babes¸-Bolyai Math., 22(1977), 40-42), (Basic problem for Maia's theorem, Sem. on Fixed Point Theory, Preprint 3(1981), Babes¸-Bolyai Univ. Cluj- Napoca, 112-115) and (Data dependence of the fixed points in a set with two metrics, Fixed Point Theory, 8(2007), no. 1, 115-123), by applying, instead of contraction principle, some variants of Maia's fixed point theorem. 2010 Mathematics Subject Classification: 47H10, 47H09, 34K05, 34K12, 45D05, 45G10, [ABSTRACT FROM AUTHOR]

In this paper, our focus is to acquaint with the Suzuki-type mappings to establish some fixed point results using the new w-interpolative approach. We present some results for interpolative contraction operators via the w-admissible maps which satisfy the Kannan, Ćirić–Reich–Rus, and Hardy–Rogers contractions in quasi-partial b-metric space. Further, the outcomes so obtained are affirmed with relevant examples. [ABSTRACT FROM AUTHOR]

Automatic text processing is now a mature discipline in computer science, and so attempts at advancements using quantum computation have emerged as the new frontier, often under the term of quantum natural language processing. The main challenges consist in finding the most adequate ways of encoding words and their interactions on a quantum computer, considering hardware constraints, as well as building algorithms that take advantage of quantum architectures, so as to show improvement on the performance of natural language tasks. In this paper, we introduce a new framework that starts from a grammar that can be interpreted by means of tensor contraction, to build word representations as quantum states that serve as input to a quantum algorithm. We start by introducing an operator measurement to contract the representations of words, resulting in the representation of larger fragments of text. We then go on to develop pipelines for the tasks of sentence meaning disambiguation and question answering that take advantage of quantum features. For the first task, we show that our contraction scheme deals with syntactically ambiguous phrases storing the various different meanings in quantum superposition, a solution not available on a classical setting. For the second task, we obtain a question representation that contains all possible answers in equal quantum superposition, and we implement Grover's quantum search algorithm to find the correct answer, agnostic to the specific question, an implementation with the potential of delivering a result with quadratic speedup. [ABSTRACT FROM AUTHOR]

This paper presents a novel numerical method for simulation controlled-source audio-magnetotellurics (CSAMT) and radio-magnetotellurics (CSRMT) data. These methods are widely used in mineral exploration. Interpretation of the CSAMT and CSRMT data collected over an area with the complex geology requires application of effective methods of numerical modeling capable to represent the geoelectrical model of a deposit well. In this paper, we considered an approach to 3D electromagnetic (EM) modeling based on new types of preconditioned iterative solvers for finite-difference (FD) EM simulation. The first preconditioner used fast direct inversion of the layered Earth FD matrix (Green's function preconditioner). The other combined the first with a contraction operator transformation. To illustrate the effectiveness of the developed numerical modeling methods, a 3D resistivity model of Aleksandrovka study area in Kaluga Region, Russia, was prepared based on drilling data, AMT, and a detailed CSRMT survey. We conducted parallel EM simulation of the full CSRMT survey. Our results indicated that the developed methods can be effectively used for modeling EM responses over a realistic complex geoelectrical model for a controlled source EM survey with hundreds of receiver stations. The contraction-operator preconditioner outperformed the Green's function preconditioner by factor of 7-10, both with respect to run-time and iteration count, and even more at higher frequencies. [ABSTRACT FROM AUTHOR]

In this paper, we introduce new concepts that relates to soft space based on work that was previously presented by researchers in this regard. First we give the definition of Soft Contraction Operator and some examples. After that we introduce the concepts of soft Picard iteration and soft Mann iteration processes. We also give some examples to illustrate them. Many concepts in normed spaces have been generalized in soft normed spaces. One of the important concepts is the concept of stability of soft iteration in soft normed spaces. We discuss this concept by giving some lemmas that are used to prove some theorems about stability of soft iteration processes (with soft contraction operator) with soft Picard iteration procedure as well as soft Mann iteration procedure. [ABSTRACT FROM AUTHOR]

This paper consists of Hankel results of ω-order reversing partial contraction as a semigroup of linear operator. Spectral mapping theorem was investigated and it was established that ω-order reversing partial contraction mapping is an eventually uniform continuous semigroup in which we showed that the proof of the extension of T(t) to a C0-semigroup ˆ T(t) on a space ˆX containing X isometrically bounded. The space is constructed in such a way that the spectrum of the generator A of T(t) coincides with the spectrum of the generator Aˆ of Tˆ(t) and the approximate point spectrum of A coincides with the point spectrum of Aˆ. [ABSTRACT FROM AUTHOR]

In this paper, we introduce some common fixed point theorems for interpolative contraction operators using Perov operator which satisfy Suzuki type mappings. Further, some results are given. These results generalize several new results present in the literature. [ABSTRACT FROM AUTHOR]

In this paper, we consider the inverse boundary value problem for a partial differential equation of third order with nonlocal boundary conditions, including an integral condition. Using analytical and operator-theoretic methods, as well as the Fourier method, the existence and uniqueness of the classical solution of this problem is proved. [ABSTRACT FROM AUTHOR]

In the context of Hilbert space operators, there is a strong relationship between convex and expansive operators and 2-isometries. In this paper, we investigate the bounded linear operators T on a Hilbert space H which have a 2-isometric lifting S on a Hilbert space K containing H as a closed subspace invariant for S ⁎ S. This last property holds in particular when S | K ⊖ H is an isometry. We relate such 2-isometric liftings S by some convex, concave or expansive liftings of the same type as S. We also examine some power bounded operators with such liftings, as well as an intermediate expansive lifting associated with T on the space H ⊕ ℓ + 2 (H). The latter notion is used to obtain 2-isometric liftings S for T (as above) and to describe the similarity of a quasi-expansive operator to a contraction. [ABSTRACT FROM AUTHOR]

In this paper, we establish the quantitative mean ergodic theorems for two subclasses of power bounded operators on a fixed noncommutative L p space with 1 < p < ∞ , which mainly concerns power bounded invertible operators and Lamperti contractions. Our approach to the quantitative ergodic theorems relies on noncommutative square function inequalities. The establishment of the latter involves several new ingredients such as the almost orthogonality and Calderón-Zygmund arguments for non-smooth kernels from semi-commutative harmonic analysis, the extension properties of the operators under consideration from operator theory, and a noncommutative version of the classical transference method due to Coifman and Weiss. [ABSTRACT FROM AUTHOR]

Recall from [2], that a mapping T : X 7→ X is called a Reich mapping if it satisfies for all x; yϵ X, d(Tx; Ty) ≤ ad(x; Tx) + bd(y; Ty) + cd(x; y), where a,b,c are nonnegative and satisfy a + b + c < 1. Alternatively, one could define a Reich mapping as follows: T : X 7→ X is called a Reich mapping if there exists a nonnegative constant k with k < 1 3 such that d(Tx; Ty) ≤ k[d(x; Tx)+d(y; Ty)+d(x; y)]. In the present paper, we address the following: How do we characterize Theorem 3 [2], when T is a non-self map? We show such a characterization is given by Theorem 3.1 or Corollary 3.2 in this paper. [ABSTRACT FROM AUTHOR]

In this paper, we prove coincidence and common fixed points results under nonlinear contractions on a metric space equipped with an arbitrary binary relation. Our results extend, generalize, modify and unify several known results especially those are contained in Berzig [J. Fixed Point Theory Appl. 12, 221-238 (2012))] and Alam and Imdad [To appear in Filomat (arXiv:1603.09159 (2016))]. Interestingly, a corollary to one of our main results under symmetric closure of a binary relation remains a sharpened version of a theorem due to Berzig. Finally, we use examples to highlight the accomplished improvements in the results of this paper. [ABSTRACT FROM AUTHOR]

In this paper, we consider a nonlinear neutral fractional difference equations. By applying Krasnoselskii's fixed point theorem, sufficient conditions for the existence of solutions are established. Also, the uniqueness of a solution is given. As an application of the main theorems, we provide the existence and uniqueness of the discrete fractional Lotka-Volterra model of neutral type. Our main results extend and generalize the results that are obtained in [6]. [ABSTRACT FROM AUTHOR]

Motivated and inspired by the growing contribution with respect to iterative approximations from some researchers in the literature, we design and investigate two types of brand-new semi-implicit viscosity iterative approximation methods for finding the fixed points of nonexpansive operators associated with contraction operators in complete CAT (0) spaces and for solving related variational inequality problems. Under some suitable assumptions, strong convergence theorems of the sequences generated by the approximation iterative methods are devised, and a numerical example and some applications to related variational inequality problems are included to verify the effectiveness and practical utility of the convergence theorems. Our main results presented in this paper do not only improve, extend and refine some corresponding consequences in the literature, but also show that the additional variational inequalities, general variational inequality systems and equilibrium problems can be solved via approximation of the iterative sequences. Finally, we provide an open question for future research. [ABSTRACT FROM AUTHOR]

In this paper, we introduce the concept of square-mean piecewise almost automorphic function. By using the theory of semigroups of operators and the contraction mapping principle, the existence of square-mean piecewise almost automorphic mild solutions for linear and nonlinear impulsive stochastic evolution equations is investigated. In addition, the exponential stability of square-mean piecewise almost automorphic mild solutions for nonlinear impulsive stochastic evolution equations is obtained by the generalized Gronwall–Bellman inequality. Finally, we provide an illustrative example to justify the results. [ABSTRACT FROM AUTHOR]

In this paper, we investigate some existence and Ulam's type stability concepts for partial fractional random differential inclusions in Banach spaces with a nonconvex valued right hand side. Our existence results are based upon Nowak's fixed point theorem for random multivalued contraction operators. [ABSTRACT FROM AUTHOR]

Purpose: The purpose of this paper is to demonstrate how collaborative contracts can improve industrial maintenance contract relationships. Design/methodology/approach: The research compares performance contracts with collaborative contracts, a new contract type whereby the contract parties align their objectives. The study uses game theory and describes the contract types as mechanism designs to compare the contract types. The mechanisms are validated with case studies. The utility of the contract types is verified with Monte Carlo simulations using expert opinions. Findings: The research demonstrates that, under certain conditions, collaborative contracts result in a higher utility than performance contracts for all contract parties. Practical implications: The use of collaborative contracts between an operator of a technical system and a maintenance organisation reduces maintenance costs and improves the availability of the technical system, increasing the utility for all contract parties. Originality/value: The collaborative contract is a new contract type for maintenance services and the research method provides a new approach to optimise industrial maintenance contract relationships. [ABSTRACT FROM AUTHOR]

In this paper, we prove the existence of fixed points for Kannan contraction, Chat- terjea contraction and Reich contraction in setting of digital metric spaces. These digital con-tractions are the applications of metric fixed point theory contractions. [ABSTRACT FROM AUTHOR]

In this paper, we introduce a new idea of best proximity point of F-contraction on a closed ball and obtain new theorems in a complete metric space. That is why this outcome becomes useful for contraction of a mapping on a closed ball instead of the whole space. At the same time, some comparative examples are constructed which establish the superiority of our results. Our results that have come into being give a proof of extension as well as substantial generalizations and improvements of several well known results in the existing comparable literature. [ABSTRACT FROM AUTHOR]

In this paper, we, motivated by Mihet [2], give the concept of two nonlinear contractions ((φ, ε-λ)-contraction and (f, bn)-contraction) in KM-fuzzy metric spaces, and obtained some fixed point theorems. We answer the open question posed by Mihet in [2, open question 2]. Finally, an example can be used to be exemplify our results. [ABSTRACT FROM AUTHOR]

In this paper, the negative proportional dynamic feedback is designed in the right boundary of the wave component of the 1-d heat-wave system coupled at the interface and the long-time behavior of the system is discussed. The system is formulated into an abstract Cauchy problem on the energy space. The energy of the system does not increase because the semigroup generated by the system operator is contracted. In the meanwhile, the asymptotic stability of the system is derived in light of the spectral configuration of the system operator. Furthermore, the spectral expansions of the system operator are precisely investigated and the asymptotical stability is not exponential and is shown in view of the spectral expansions. [ABSTRACT FROM AUTHOR]

In this paper, we obtain some coupled fixed point results for two mappings satisfying some contractive conditions in cone b-metric spaces over Banach algebras with a solid cone by virtue of the properties of spectral radius. Also we give an example as an applications of one of the main results. [ABSTRACT FROM AUTHOR]

The purpose of the paper is to obtain estimates for differences of functions of two pairs of commuting contractions on Hilbert space. In particular, Lipschitz type estimates, Hölder type estimates, Schatten–von Neumann estimates are obtained. The results generalize earlier known results for functions of self‐adjoint operators, normal operators, contractions and dissipative operators. [ABSTRACT FROM AUTHOR]