Arabian Journal of Mathematics最新文献

In this paper, we investigate the generalization of Hermite-Hadamard-type orthogonality within skew structures. Moslehian and Rassias (Commun Math Anal 8:16–21, 2010) characterized inner product spaces by employing the parallelogram law for skew structures in their research. We introduce the concept of skew orthogonality by integrating the parallelogram law of skew structures with Hermite-Hadamard-type orthogonality and discuss its properties. Finally, we characterize inner product spaces using mappings that preserve skew orthogonality.

The different systems of Sylvester quaternion matrix equations have prolific functions in system and control. This paper considers a Hermitian solution of a system of Sylvester quaternion matrix equations over a quaternion algebra (mathbb {H}). If some necessary and sufficient conditions are fulfilled, the general solution to these quaternion matrix equations is expressed by explicit representation formulas in terms of generalized inverses. We provide an algorithm and a numerical example based on the original direct method using determinantal representations of the quaternion Moore–Penrose inverse.

In this article, we study one, two and three-dimensional nonlinear elastic wave equations using quadratically nonlinear Murnaghan potential. We employ two effective methods for obtaining approximate series solutions the Adomian decomposition and the variational iteration method. These methods have the advantage of not requiring any physical parametric assumptions in the problem. Finally, these methods can generate expansion solutions for linear and nonlinear differential equations without perturbation, linearization, or discretization. The results obtained using the adopted methods along various initial and boundary conditions are in excellent agreement with the numerical results on MATLAB, which show the reliability of our methods to these problems. We came to the conclusion that our methods are accurate and simple to use.

A balancing-like sequence is a binary recurrence sequence which generalizes the balancing sequence and the sequence of nonnegative integers. This sequence, under certain assumptions, may be used to describe the growth of fortune of a person engaged in some business or profession. Since, in any business or profession, the growth is influenced by many uncertainties, it is more natural to induce some sort of randomness in the balancing-like sequences. If, in a balancing-like sequence, the growth rate is assumed to be a random variable, the resulting sequence will be a stochastic process and the sequence of expectations, in many cases, cannot be described as a binary recurrence sequence. In some cases, the growth rate of expectations increases without limit while, in some cases, it remains finite.

In this paper, we consider the two Hecke groups (G_{4}) and (G_{6}) and we use the Schmidt Subspace Theorem to establish the transcendence of some quasi-periodic Rosen continued fractions in order to get the exact analogues of the results established with the regular continued fractions.

The normalized Ricci flow converges to a constant curvature metric for a connected Kaehlerian slant submanifold in a complex space form if the squared norm of the second fundamental form satisfies certain upper bounds. These bounds include the constant sectional curvature, the slant angle, and the squared norm of the mean curvature vector. Additionally, we demonstrate that the submanifold is diffeomorphic to the sphere (mathbb {S}^{n_1}) under some restriction on the mean curvature. We claim that some of our previous results are rare cases.

In this paper we propose new averaged iterative algorithms designed for solving a split common fixed point problem in the class of demicontractive mappings. The algorithms are obtained by inserting an averaged term into the algorithms used in [Li, R. and He, Z., A new iterative algorithm for split solution problems of quasi-nonexpansive mappings J. Inequal. Appl. 131 (2015), 1–12.] for solving the same problem but in the class of quasi-nonexpansive mappings, which is a subclass of demicontractive mappings. Basically, our investigation is based on the embedding of demicontractive operators in the class of quasi-nonexpansive operators by means of averaged mappings. For the considered algorithms we prove weak and strong convergence theorems in the setting of a real Hilbert space. A numerical example is given to illustrate the results.

This paper extends the study of the generalized Lorentz spaces to the Lorentz–Herz spaces. The Lorentz–Herz spaces consist of all Lebesgue measurable functions such that theirs non-increasing rearrangements belong to the weighted Herz space. The main result of this paper establishes the mapping properties of the Hardy–Littlewood maximal function on the Lorentz–Herz spaces.

In this article, we investigate the asymptotic behavior of the Mindlin–Timoshenko system under the influence of nonlinear dissipation affecting the rotation angle equations. Initially, we provide a concise review of the system’s solution existence. Subsequently, we demonstrate that the energy associated with the solution of the Mindlin–Timoshenko setup follows a dissipation. Furthermore, under the condition of equal wave speeds, we establish a comprehensive decay theorem for the energy, offering explicit insights into its general behavior.

Symmetric spaces arise in wide variety of problems in Mathematics and Physics. They are mostly studied in Representation theory, Harmonic analysis and Differential geometry. As many physical systems have symmetric spaces as their configuration spaces, the study of controllability on symmetric space is quite interesting. In this paper, a driftless control system of type ({dot{x}}= sum _{i=1}^m u_if_i(x)) is considered on a symmetric space. For this we have established global controllability condition which is illustrated by few examples of exponential submanifolds of SE(3) and random matrix ensembles.