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Let ℓ be a Banach sequence space with a monotone norm in which the canonical system (en) is an unconditional basis. We show that if there exists a continuous linear unbounded operator between ℓ -Köthe spaces, then there exists a continuous unbounded quasidiagonal operator between them. Using this result, we study the corresponding Köthe matrices when every continuous linear operator between ℓ -Köthe spaces is bounded. As an application, we observe that the existence of an unbounded operator between ℓ -Köthe spaces, under a splitting condition, causes the existence of a common basic subspace. [ABSTRACT FROM AUTHOR]

Collage Theorem provides a bound for the distance between an element of a given space and a fixed point of a self-map on that space, in terms of the distance between the point and its image. We give in this paper some results of Collage type for Reich mutual contractions in b-metric and strong b-metric spaces. We give upper and lower bounds for this distance, in terms of the constants of the inequality involved in the definition of the contractivity. Reich maps contain the classical Banach contractions as particular cases, as well as the maps of Kannan type, and the results obtained are very general. The middle part of the article is devoted to the invertibility of linear operators. In particular we provide criteria for invertibility of operators acting on quasi-normed spaces. Our aim is the extension of the Casazza-Christensen type conditions for the existence of inverse of a linear map defined on a quasi-Banach space, using different procedures. The results involve either a single map or two operators. The latter case provides a link between the properties of both mappings. The last part of the article is devoted to study the construction of fractal curves in Bochner spaces, initiated by the first author in a previous paper. The objective is the definition of fractal curves valued on Banach spaces and Banach algebras. We provide further results on the fractal convolution of operators, defined in the same reference, considering in this case the nonlinear operators. We prove that some properties of the initial maps are inherited by their convolutions, if some conditions on the elements of the associated iterated function system are satisfied. In the last section of the paper we use the invertibility criteria given before in order to obtain perturbed fractal spanning systems for quasi-normed Bochner spaces composed of Banach-valued integrable maps. These results can be applied to Lebesgue spaces of real valued functions as a particular case. [ABSTRACT FROM AUTHOR]

The present paper deals with the approximation properties of the linear positive operators, including Δh -Gould-Hopper Appell polynomials. We investigate some theorems for convergence of the operators and their approximation degrees with the help of the classical approach, Peetre's K-functional, Lipschitz class and Voronovskajatype theorem. In the last section of the paper, we introduce the Kantorovich form of the operators and examine the approximation degree. [ABSTRACT FROM AUTHOR]

The aim of this paper is to establish several versions of Paley–Wiener-type theorems for the canonical Fourier–Bessel transform, which is a Bessel type of linear canonical transform indexed by a matrix parameter m ∈ SL(2, ℝ). [ABSTRACT FROM AUTHOR]

In this paper, we investigate a class of hierarchical variational inequalities (HVIPs, i.e., strongly monotone variational inequality problems defined on the solution set of multiple-set split common fixed-point problems) with quasi-pseudocontractive mappings in real Hilbert spaces, with special cases being able to be found in many important engineering practical applications, such as image recognizing, signal processing, and machine learning. In order to solve HVIPs of potential application value, inspired by the primal-dual algorithm, we propose a novel accelerated cyclic iterative algorithm that combines the inertial method with a correction term and a self-adaptive step-size technique. Our approach eliminates the need for prior knowledge of the bounded linear operator norm. Under appropriate assumptions, we establish strong convergence of the algorithm. Finally, we apply our novel iterative approximation to solve multiple-set split feasibility problems and verify the effectiveness of the proposed iterative algorithm through numerical results. [ABSTRACT FROM AUTHOR]

This research explores the interplay between violator spaces and greedoids—two distinct theoretical frameworks developed independently. Violator spaces were introduced as a generalization of linear programming, while greedoids were designed to characterize combinatorial structures where greedy algorithms yield optimal solutions. These frameworks have, until now, existed in isolation. This paper bridges the gap by showing that greedoids can be defined using a modified violator operator. The established connections not only deepen our understanding of these theories but also provide a new characterization of antimatroids. [ABSTRACT FROM AUTHOR]

In this paper, we introduce several new types of partial fractional derivatives in the continuous setting and the discrete setting. We analyze some classes of the abstract fractional differential equations and the abstract fractional difference equations depending on several variables, providing a great number of structural results, useful remarks and illustrative examples. Concerning some specific applications, we would like to mention here our investigation of the fractional partial differential inclusions with Riemann–Liouville and Caputo derivatives. We also establish the complex characterization theorem for the multidimensional vector-valued Laplace transform and provide certain applications. [ABSTRACT FROM AUTHOR]

In this paper, a generic fractional derivative is defined as a set of the linear operators left-inverse to the Riemann–Liouville fractional integral. Then, the theory of the left-invertible operators developed by Przeworska-Rolewicz is applied to deduce its properties. In particular, we characterize its domain, null-space, and projector operator; establish the interrelations between its different realizations; and present a generalized fractional Taylor formula involving the generic fractional derivative. Then, we consider the fractional relaxation equation containing the generic fractional derivative, derive a closed-form formula for its unique solution, and study its complete monotonicity. [ABSTRACT FROM AUTHOR]

In this paper, we prove that every bounded linear operator on a separable Hilbert space has a non-trivial invariant subspace. This answers the well-known invariant subspace problem. [ABSTRACT FROM AUTHOR]

In this paper, we employ a generalization of the Boas–Bellman inequality for inner products, as developed by Mitrinović–Pečarić–Fink, to derive several upper bounds for the 2 p -th power with p ≥ 1 of the numerical radius of the off-diagonal operator matrix 0 A B * 0 for any bounded linear operators A and B on a complex Hilbert space H. While the general matrix is not symmetric, a special case arises when B = A * , where the matrix becomes symmetric. This symmetry plays a crucial role in the derivation of our bounds, illustrating the importance of symmetric structures in operator theory. [ABSTRACT FROM AUTHOR]

This paper presents the Mann-type inertial accelerated subgradient extragradient algorithm with non-monotonic step sizes for solving the split equilibrium and fixed point problems relating to pseudomonotone and Lipschitz-type continuous bifunctions and nonexpansive mappings in the framework of real Hilbert spaces. By sufficient conditions on the control sequences of the parameters of concern, the strong convergence theorem to support the proposed algorithm, which involves neither prior knowledge of the Lipschitz constants of bifunctions nor the operator norm of the bounded linear operator, is demonstrated. Some numerical experiments are performed to show the efficacy of the proposed algorithm. [ABSTRACT FROM AUTHOR]

This paper investigates the Li–Yorke chaos in linear systems with weak topology on Hilbert spaces. A weak topology induced by bounded linear functionals is first constructed. Under this weak topology, it is shown that the weak Li–Yorke chaos can be equivalently measured by an irregular or a semi-irregular vector, which are utilized to establish criteria for the weak Li–Yorke chaos of diagonalizable operators, Jordan blocks, and upper triangular operators. In particular, for a linear operator that can be decomposed into a direct sum of finite-dimensional Jordan blocks, it is Li–Yorke chaotic in weak topology if its point spectrum contains a pair of real opposite eigenvalues with absolute values not less than 1, or a pair of complex conjugate eigenvalues with moduli not less than 1. Interestingly, as a specific example of upper triangular operator, the existence of Li–Yorke chaos in weak topology can be derived for a class of linear operators expressed as the direct sum of finite-dimensional Jordan blocks and a strongly irreducible operator. [ABSTRACT FROM AUTHOR]

In this paper, we aimed to identify the dynamics of a crude distillation unit (CDU) using closed-loop data with NARX−NN and the Koopman operator in both linear (KL) and bilinear (KB) forms. A comparative analysis was conducted to assess the performance of each method under different experimental conditions, such as the gain, a delay and time constant mismatch, tight constraints, nonlinearities, and poor tuning. Although NARX−NN showed good training performance with the lowest Mean Squared Error (MSE), the KB demonstrated better generalization and robustness, outperforming the other methods. The KL observed a significant decline in performance in the presence of nonlinearities in inputs, yet it remained competitive with the KB under other circumstances. The use of the bilinear form proved to be crucial, as it offered a more accurate representation of CDU dynamics, resulting in enhanced performance. [ABSTRACT FROM AUTHOR]

Let n ∈ N 0 , ψ be an analytic self-map on D and u be an analytic function on D. The single operator D u , ψ n acting on various spaces of analytic functions has been a subject of investigation for many years. It is defined as (D u , ψ n f) (z) = u (z) f (n) (ψ (z)) , f ∈ H (D) . However, the study of the operator P u → , ψ k , which represents a finite sum of these operators with varying orders, remains incomplete. The boundedness, compactness and essential norm of the operator P u → , ψ k on the Bloch space are investigated in this paper, and several characterizations for these properties are provided. [ABSTRACT FROM AUTHOR]

In this short note we indicate some improvement of an article published in this journal by Crespo, Ivorra and Ramos 6. The techniques used are connected with several smoothing effects associated with linear partial differential operators which give rise to some accretive operators in L¹(Ω), as well as with some H²(Ω) estimates independent on time. [ABSTRACT FROM AUTHOR]

In this article, the symmetric operator L corresponding to the boundary value problem is represented as the difference of two commuting operators A and  B.  The uniqueness of the solution is guaranteed if the spectra of the operators A and B do not intersect and the domain of the operator B is given by non-degenerate boundary conditions. In contrast to the existing papers, the criterion for the uniqueness of the boundary value problem formulated in this paper is satisfied even when the system of root functions of the operator B does not form a basis in the corresponding space. At the same time, only the closedness of the linear operator A is required. [ABSTRACT FROM AUTHOR]

In this paper, we investigate a general maximum principle for discrete fractional stochastic difference system of mean‐field type. The admissible control domain is nonconvex. We give Malliavin calculus for discrete‐time case to deal with the fractional terms. The maximum principle of general type is derived by classical variation and linear operator methods. In addition, a linear‐quadratic problem is solved to illustrate the main result and we also figure out a numerical result in this case. [ABSTRACT FROM AUTHOR]

This paper introduces a new idea to obtain a better order of approximation for the Baskakov operator. We conclude two new operators from orders one and two of the Baskakov type. Also, we prove some directed results concerning the rate of convergence of these operators. We apply the Maple software to demonstrate how the operators converge to a specific function. [ABSTRACT FROM AUTHOR]

Let H be a complex Hilbert space and let T represent a bounded linear operator on H. In this paper we introduce, a new class of non normal operators, the (M, k)-quasi paranormal operator. An operator T is said to be a (M,k)-quasi paranormal operator, for a non negative integer k and a real positive number M if it satisfies ||Tk+1x||2 < M||Tk+2x|| ||Tkx||, for all x ∈ H. This new class of operators is generalization of some of the non normal operators, such as, the k-quasi paranormal and M-paranormal operators. We prove the basic properties, the structural and spectral properties and also the matrix representation of this new class of operators. [ABSTRACT FROM AUTHOR]

This paper considers a system with one robot and n safety units (one of which works while the others remain on standby), which is described by an integro-deferential equation. The system can fail in the following three ways: fails with an incident, fails safely and fails due to the malfunction of the robot. Using the C 0 – semigroups theory of linear operators, we first show that the system has a unique non-negative, time-dependent solution. Then, we obtain the exponential convergence of the time-dependent solution to its steady-state solution. In addition, we study the asymptotic behavior of some time-dependent reliability indices and present a numerical example demonstrating the effects of different parameters on the system. [ABSTRACT FROM AUTHOR]

This paper concerns with the existence of radial solutions of the biharmonic elliptic equation ▵ 2 u = f (| x | , u , | ∇ u | , ▵ u) in an annular domain Ω = { x ∈ R N : r 1 < | x | < r 2 } ( N ≥ 2 ) with the boundary conditions u | ∂ Ω = 0 and ▵ u | ∂ Ω = 0 , where f : [ r 1 , r 2 ] × R × R + × R → R is continuous. Under certain inequality conditions on f involving the principal eigenvalue λ 1 of the Laplace operator − ▵ with boundary condition u | ∂ Ω = 0 , an existence result and a uniqueness result are obtained. The inequality conditions allow for f (r , ξ , ζ , η) to be a superlinear growth on ξ , ζ , η as | (ξ , ζ , η) | → ∞ . Our discussion is based on the Leray–Schauder fixed point theorem, spectral theory of linear operators and technique of prior estimates. [ABSTRACT FROM AUTHOR]

In this paper, we study the existence of positive solutions for a changing-sign perturbation tempered fractional model with weak singularity which arises from the sub-diffusion study of anomalous diffusion in Brownian motion. By two-step substitution, we first transform the higher-order sub-diffusion model to a lower-order mixed integro-differential sub-diffusion model, and then introduce a power factor to the non-negative Green function such that the linear integral operator has a positive infimum. This innovative technique is introduced for the first time in the literature and it is critical for controlling the influence of changing-sign perturbation. Finally, an a priori estimate and Schauder's fixed point theorem are applied to show that the sub-diffusion model has at least one positive solution whether the perturbation is positive, negative or changing-sign, and also the main nonlinear term is allowed to have singularity for some space variables. [ABSTRACT FROM AUTHOR]

This study takes a detailed look at various inequalities related to the Euclidean operator radius. It examines groups of n-tuple operators, studying how they add up and multiply together. It also uncovers a unique power inequality specific to the Euclidean operator radius. The research broadens its scope to analyze how n-tuple operators, when used as parts of 2 × 2 operator matrices, illustrate inequalities connected to the Euclidean operator radius. By using the Euclidean numerical radius and Euclidean operator norm for n-tuple operators, the study introduces a range of new inequalities. These inequalities not only set limits for the addition, multiplication, and Euclidean numerical radius of n-tuple operators but also help in establishing inequalities for the Euclidean operator radius. This process involves carefully examining the Euclidean numerical radius inequalities of 2 × 2 operator matrices with n-tuple operators. Additionally, a new inequality is derived, focusing specifically on the Euclidean operator norm of 2 × 2 operator matrices. Throughout, the research keeps circling back to the idea of finding and understanding symmetries in linear operators and matrices. The paper highlights the significance of symmetry in mathematics and its impact on various mathematical areas. [ABSTRACT FROM AUTHOR]

In this paper, a novel Model Predictive Control (MPC) technique for multi-satellite formation flying geometry acquisition and maintenance in high-drag environment is presented. The proposed MPC relies on a linearized and convexified quasi-nonsingular Relative Orbital Elements (ROE) model based on state transition matrices propagation, allowing to include the effect of perturbations in the prediction to optimize fuel efficiency and tracking accuracy. The formation is controlled with respect to a non-decaying orbiting point to perform absolute and relative station keeping simultaneously. For this purpose, a new dedicated plant matrix to include drag effects on ROE in the propagation is derived and validated with respect to numerical results. In all simulations, the satellites are assumed to be equipped with a single low-thrust propulsion unit, therefore, specific constraints are included in the controller to obtain a feasible solution in a real operational scenario. Moreover, a collision avoidance constraint is added in case of close proximity operations exploiting a linear mapping between the set of ROE and cartesian coordinates expressed in the Local-Vertical-Local-Horizontal (LVLH) reference frame. The controller response is simulated in several realistic mission contexts with a high-fidelity orbital propagator and the results are validated for fuel efficiency by comparing them to similar approaches available in literature and to optimal solutions obtained respectively with a direct single shooting algorithm and with a closed-form impulsive formulation. [ABSTRACT FROM AUTHOR]

In this paper, a modification of general linear positive operators introduced by Ibragimov and Gadjiev in 1970 is constructed. It is shown that this modification preserves exponential mappings and also contains modified Bernstein-, Szász- and Baskakov-type operators as special cases. The convergence properties of corresponding operators on [ 0 , ∞) and in exponentially weighted spaces are investigated. Finally, the quantitative Voronovskaja theorem in terms of modulus of continuity for functions having exponential growth is examined. [ABSTRACT FROM AUTHOR]

In this paper, we initiate the study of a new interrelation between linear ordinary differential operators and complex dynamics which we discuss in detail in the simplest case of operators of order 1. Namely, assuming that such an operator T has polynomial coefficients, we interpret it as a continuous family of Hutchinson operators acting on the space of positive powers of linear forms. Using this interpretation of T , we introduce its continuously Hutchinson invariant subsets of the complex plane and investigate a variety of their properties. In particular, we prove that for any T with non-constant coefficients, there exists a unique minimal under inclusion invariant set M C H T and find explicitly what operators T have the property that M C H T = C. [ABSTRACT FROM AUTHOR]

Direction-splitting implicit solvers employ the regular structure of the computational domain augmented with the splitting of the partial differential operator to deliver linear computational cost solvers for time-dependent simulations. The finite difference community originally employed this method to deliver fast solvers for PDE-based formulations. Later, this method was generalized into so-called variational splitting. The tensor product structure of basis functions over regular computational meshes allows us to employ the Kronecker product structure of the matrix and obtain linear computational cost factorization for finite element method simulations. These solvers are traditionally used for fast simulations over the structures preserving the tensor product regularity. Their applications are limited to regular problems and regular model parameters. This paper presents a generalization of the method to deal with non-regular material data in the variational splitting method. Namely, we can vary the material data with test functions to obtain a linear computational cost solver over a tensor product grid with non-regular material data. Furthermore, as described by the Maxwell equations, we show how to incorporate this method into finite element method simulations of non-stationary electromagnetic wave propagation over the human head with material data based on the three-dimensional MRI scan. [ABSTRACT FROM AUTHOR]

Let A be a unital Banach algebra with unit e, M be a Banach A-bimodule, and w ∈ A . In this paper, we characterize those continuous linear maps δ : A → M that satisfy one of the following conditions: δ (a b) = δ (a) b + a δ (b) , 2 δ (w) = δ (a) b + a δ (b) , δ (a b) = δ (a) b + a δ (b) - a δ (e) b , for any a , b ∈ A with a b = b a = w , where w is either a separating point with w ∈ Z (A) or an idempotent. [ABSTRACT FROM AUTHOR]

The aim of this paper is to define the linear operator based on the generalized Mittag-Leffler function and the Lambert series. By using this operator, we introduce a new subclass of β-uniformly starlike functions Τ J (α i) . Further, we obtain coefficient estimates, convex linear combinations, and radii of close-to-convexity, starlikeness, and convexity for functions f ∈ Τ J (α i) . In addition, we investigate the inclusion conditions of the Hadamard product and the integral transform. Finally, we determine the second Hankel inequality for functions belonging to this subclass. [ABSTRACT FROM AUTHOR]

The conventional approach of the local convergence analysis of an iterative method on R m , with m a natural number, depends on Taylor series expansion. This technique often requires the calculation of high-order derivatives. However, those derivatives may not be part of the proposed method(s). In this way, the method(s) can face several limitations, particularly the use of higher-order derivatives and a lack of information about a priori computable error bounds on the solution distance or uniqueness. In this paper, we address these drawbacks by conducting the local convergence analysis within the broader framework of a Banach space. We have selected an important family of high convergence order methods to demonstrate our technique as an example. However, due to its generality, our technique can be used on any other iterative method using inverses of linear operators along the same line. Our analysis not only extends in R m spaces but also provides convergence conditions based on the operators used in the method, which offer the applicability of the method in a broader area. Additionally, we introduce a novel semilocal convergence analysis not presented before in such studies. Both forms of convergence analysis depend on the concept of generalized continuity and provide a deeper understanding of convergence properties. Our methodology not only enhances the applicability of the suggested method(s) but also provides suitability for applied science problems. The computational results also support the theoretical aspects. [ABSTRACT FROM AUTHOR]

In the previous paper Liu and Pu (2019) [17] , we proved the nonlinear Schrödinger (NLS) approximation for the Euler-Poisson system for a hot ion-acoustic plasma, where the appearance of resonances and the loss of derivatives of quadratic terms are the main difficulties. Note that when the ion-acoustic plasma is hot, the Euler-Poisson system is Friedrich symmetrizable, and the linear term can provide a derivative to compensate the loss of derivative induced by quadratic terms after diagonalizing the linearized system. When the ion-acoustic plasma is cold, as considered in the present paper, the situation is very different from that in the previous paper. The Euler-Poisson system becomes a pressureless system, so the linear operator has no regularity, and the quadratic terms still lose a derivative in the diagonalized system. This fact makes it more difficult to prove the NLS approximation of Euler-Poisson system for a cold ion-acoustic plasma. In this paper, we take advantage of the special structure of the pressureless Euler-Poisson system and the normal-form transformation to deal with the difficulties caused by resonances, especially the difficulties caused by derivative loss, in order to prove the NLS approximation. [ABSTRACT FROM AUTHOR]

The authors of the present paper previously proved the Ulam stability for the n-th-order linear differential operator with constant coefficients. They obtained its best Ulam constant for the case of distinct roots of the characteristic equation. However, a complete answer to the problem of the best Ulam constant was later obtained only for the second-order linear differential operator. This paper deals with the Ulam stability of the third-order linear differential operator with constant coefficients acting in a Banach space. The paper's main purpose is to obtain the best Ulam constant of this operator, thus completing the previous research in the field. [ABSTRACT FROM AUTHOR]

The atmosphere and ocean are described by highly oscillatory PDEs that challenge both our understanding of their dynamics and their numerical approximation. This paper presents a preliminary numerical study of one type of phase averaging applied to mean flows in the 2D Boussinesq equations that also has application to numerical methods. The phase averaging technique, well-known in dynamical systems theory, relies on a mapping using the exponential operator, and then an averaging over the phase. The exponential operator has connections to the Craya–Herring basis pioneered by Jack Herring to study the fluid dynamics of oscillatory, nonlinear fluid dynamics. In this paper, we perform numerical experiments to study the effect of this averaging technique on the time evolution of the solution. We explore its potential as a definition for mean flows. We also show that, as expected from theory, the phase-averaging method can reduce the magnitude of the time rate of change in the PDEs, making them potentially suitable for time stepping methods. [ABSTRACT FROM AUTHOR]

From the previous work, when solving the LQ optimal control problem with random coefficients (SLQ, for short), it is remarkably shown that the solution of the backward stochastic Riccati equations is not regular enough to guarantee the robustness of the feedback control. As a generalization of SLQ, interesting questions are, "how about the situation in the differential game?", "will the same phenomenon appear in SLQ?". This paper will provide the answers. In this paper, we consider a closed-loop two-person zero-sum LQ stochastic differential game with random coefficients (SDG, for short) and generalize the results of Lü–Wang–Zhang into the stochastic differential game case. Under some regularity assumptions, we establish the equivalence between the existence of the robust optimal feedback control strategy operators and the solvability of the corresponding backward stochastic Riccati equations, which leads to the existence of the closed-loop saddle points. On the other hand, the problem is not closed-loop solvable if the solution of the corresponding backward stochastic Riccati equations does not have the needed regularity. [ABSTRACT FROM AUTHOR]

This paper introduces the concept of Kato chaos to linear dynamics and its induced dynamics. This paper investigates some properties of Kato chaos for a continuous linear operator T and its induced operators T ¯ . The main conclusions are as follows: (1) If a linear operator is accessible, then the collection of vectors whose orbit has a subsequence converging to zero is a residual set. (2) For a continuous linear operator defined on Fréchet space, Kato chaos is equivalent to dense Li–Yorke chaos. (3) Kato chaos is preserved under the iteration of linear operators. (4) A sufficient condition is obtained under which the Kato chaos for linear operator T and its induced operators T ¯ are equivalent. (5) A continuous linear operator is sensitive if and only if its inducing operator T ¯ is sensitive. It should be noted that this equivalence does not hold for nonlinear dynamics. [ABSTRACT FROM AUTHOR]

This paper establishes sharp local regularity estimates for viscosity solutions of fully nonlinear parabolic free boundary problems with singular absorption terms. The main difficulties are due to the blow-up of the source along the free boundary and the lack of a variational structure. The proof combines the power of the Ishii-Lions method with intrinsically parabolic oscillation estimates. The results are new, even for second-order linear operators in nondivergence form. [ABSTRACT FROM AUTHOR]

In this paper, the Parseval K - g -frames are constructed from a given K - g -frame by scaling the elements of the K - g -frame with the help of diagonal operators, and these frames are named scalable K - g -frames. Also, we prove some properties of scalable K - g -frames and construct new scalable K - g -frames from a given K - g -frame. The necessary and sufficient conditions for a K - g -frame to be scalable are given. Further, equivalent conditions for the scalability of K - g -frames and the K -frames induced by K - g -frames are obtained. Finally, it is shown that the direct sum of two scalable K - g -frames is again a scalable K - g -frame for some suitable bounded linear operator K. [ABSTRACT FROM AUTHOR]

Iterative algorithms requiring the computationally expensive in general inversion of linear operators are difficult to implement. This is the reason why hybrid Newton-like algorithms without inverses are developed in this paper to solve Banach space-valued nonlinear equations. The inverses of the linear operator are exchanged by a finite sum of fixed linear operators. Two types of convergence analysis are presented for these algorithms: the semilocal and the local. The Fréchet derivative of the operator on the equation is controlled by a majorant function. The semi-local analysis also relies on majorizing sequences. The celebrated contraction mapping principle is utilized to study the convergence of the Krasnoselskij-like algorithm. The numerical experimentation demonstrates that the new algorithms are essentially as effective but less expensive to implement. Although the new approach is demonstrated for Newton-like algorithms, it can be applied to other single-step, multistep, or multipoint algorithms using inverses of linear operators along the same lines. [ABSTRACT FROM AUTHOR]

In this paper, by using the structure properties of algebras and the technique of matrix operation, we investigate the structure of local Lie triple derivations on triangular algebras. Under some mild conditions, we prove that each local Lie triple derivation of triangular algebras can be expressed as the sum of a derivation and a linear map from the triangular algebra to its center that vanishes at Lie triple products. Finally, we apply the main result to the problem of characterizing local Lie triple derivations on an upper triangular matrix algebra. [ABSTRACT FROM AUTHOR]

In this paper, two Halpern-type inertial iteration methods with self-adaptive step size are proposed for estimating the solution of split common null point problems ( S p CNPP ) in such a way that the Halpern iteration and inertial extrapolation are computed simultaneously in the beginning of each iteration. We prove the strong convergence of sequences driven by the suggested methods without estimating the norm of bounded linear operator when certain appropriate assumptions are made. We demonstrate the efficiency of our iterative methods and compare them with some related and well-known results using relevant numerical examples. [ABSTRACT FROM AUTHOR]

Considering a piecewise smooth map describing the behavior of a pulse-modulated control system, we discuss border-collision related phenomena. We show that in the parameter space which corresponds to the domain of oscillatory mode a mapping is piecewise linear continuous. It is well known that in piecewise linear maps, classical bifurcations, for example, period doubling, tangent, fold bifurcations become degenerate ("degenerate bifurcations"), combining the properties of both smooth and border-collision bifurcations. We found unusual properties of this map, that consist in the fact that border-collision bifurcations of codimension one, including degenerate ones, occur when a pair of points of a periodic orbit simultaneously collides with two switching manifolds. This paper also discuss bifurcations of chaotic attractors such as merging and expansion ("interior") crises, associated with homoclinic bifurcations of unstable periodic orbits. [ABSTRACT FROM AUTHOR]

In this paper, the derivation of the 2-point Fractional Block Backward Differentiation Formula is studied and used to solve the fractional Pharmacokinetics model. The method is developed using the fractional linear multistep method connected to the linear difference operator. The analysis of the method's stability properties confirms that the stability regions appear to be A-stable for various values of fractional order a. Numerical results obtained using the proposed method are investigated. Additionally, the impact of fractional order on the quantity of the drug within the human body is examined. [ABSTRACT FROM AUTHOR]

This paper focuses on the spectral analysis of equations that describe the oscillations of a heavy pendulum partially filled with a homogeneous incompressible viscoelastic fluid. The constitutive equation of the fluid follows the simpler Oldroyd model. By examining the eigenvalues of the linear operator that describes the dynamics of the coupled system, it was demonstrated that under appropriate assumptions the equilibrium configuration remains stable in the linear approximation. Moreover, when the viscosity coefficient is sufficiently large the spectrum comprises three branches of eigenvalues with potential cluster points at 0 , β and ∞ where β represents the viscoelastic parameter of the fluid. These three branches of eigenvalues correspond to frequencies associated with various types of waves. This paper focuses on the spectral analysis of equations that describe the oscillations of a heavy pendulum partially filled with a homogeneous incompressible viscoelastic fluid. The constitutive equation of the fluid follows the simpler Oldroyd model. By examining the eigenvalues of the linear operator that describes the dynamics of the coupled system, it was demonstrated that under appropriate assumptions the equilibrium configuration remains stable in the linear approximation. Moreover, when the viscosity coefficient is sufficiently large the spectrum comprises three branches of eigenvalues with potential cluster points at , and where represents the viscoelastic parameter of the fluid. These three branches of eigenvalues correspond to frequencies associated with various types of waves. [ABSTRACT FROM AUTHOR]

It is well known that via the augmented Lagrangian method, one can solve Stokes' system by solving the nearly incompressible linear elasticity equation. In this paper, we show that the converse holds, and approximate the inverse of the linear elasticity operator with a convex linear combination of parameter-free operators. In such a way, we construct a uniform preconditioner for linear elasticity for all values of the Lamé parameter λ ∈ [ 0 , ∞). Numerical results confirm that by using inf-sup stable finite-element spaces for the solution of Stokes' equations, the proposed preconditioner is robust in λ. [ABSTRACT FROM AUTHOR]

In this paper, we study the stability, controllability, and differential game of pursuit for an infinite system of linear ODEs in ℓ2. The system we consider has a special right-hand side, which is not diagonal and serves as a toy model for controllable system of infinitely many interacting points. We impose integral constraints on the control parameters. We obtain criteria for stability and null controllability of the system. Further, we construct a strategy for the pursuer that guarantees completion of the pursuit problem for the differential game. To prove controllability we use the so called Gramian operators. [ABSTRACT FROM AUTHOR]

In the present paper we define the degree of nondensifiability (DND for short) of a bounded linear operator T on a Banach space and analyze its properties and relations with the Hausdorff measure of noncompactness (MNC for short) of T. As an application of our results, we have obtained a formula to find the essential spectral radius of a bounded operator T on a Banach space as well as we have provided the best possible lower bound for the Hyers-Ulam stability constant of T in terms of the aforementioned DND. [ABSTRACT FROM AUTHOR]

The Rao–Nakra sandwich beam is a coupled system consisting of two wave equations for the longitudinal displacements of the top and bottom layers and an Euler–Bernoulli beam equation for the transversal displacement. This paper concerns the system's stability when the Kelvin–Voigt damping terms act on the first and third equations. Using the semigroup theory of linear operators, we prove the global well-posedness of the associated initial boundary value problem. And then, we prove the lack of exponential stability of the system. Because of this lack of exponential stability, we study the polynomial stability and prove that the system decays with rate t − 1 4 . We further prove that this decay rate is optimal. [ABSTRACT FROM AUTHOR]

In this paper, we study regular and Fredholm solvability of a Neumann type boundary value problem for a second order elliptic type equation with operator coefficients for a separable Hilbert space on a finite domain. The conditions of regular and Fredholm solvability for the given problem in terms of only the coefficients of the equation are found. The estimates for intermediate derivatives operators are obtained. These estimates determine the solvability conditions for our problem. Note that the considered operator equations have variable coefficients. [ABSTRACT FROM AUTHOR]

In this paper, we introduce a new algorithm for solving split feasibility problems in Hilbert spaces. The algorithm stems from the relaxed CQ method and the alternated inertial step method. The proposed algorithm uses variable step-sizes which are updated at each iteration by a cheap computation without linesearch. This step-size rule allows the resulting algorithm to work more easily without the prior knowledge of the operator norm. Numerical experiments are implemented to illustrate the theoretical results and also to compare with existing algorithms. [ABSTRACT FROM AUTHOR]

The purpose of the present paper is to introduce and investigate new subclasses of analytic function class of bi-univalent functions defined in open unit disks connected with a linear q-convolution operator, which are associated with quasi-subordination. We find coefficient estimates of h 2 ,   h 3 for functions in these subclasses. Several known and new consequences of these results are also pointed out. There is symmetry between the results of the subclass f q , ∑   μ (ζ , n , ρ , σ , ϑ , γ , δ , φ) and the results of the subclass ℵ ∑ q , δ λ , ζ , n , ρ , σ , ϑ , φ . [ABSTRACT FROM AUTHOR]