Arabian Journal of Mathematics最新文献

The notion of approximate fixed point sequence, emphasized in Chidume (Geometric properties of Banach spaces and nonlinear iterations. Lecture Notes in Mathematics, 1965. Springer-Verlag London, Ltd., London, 2009), is a very useful tool in proving convergence theorems for fixed point iterative schemes in the class of nonexpansive-type mappings. In the present paper, our aim is to present simple and unified alternative proofs of some classical fixed point theorems emerging from Banach contraction principle, by using a technique based on the concepts of approximate fixed point sequence and graphic contraction.

After an overview of uses and explorations of minimal automorphic ordered sets, we present a criterion when certain superpositions of crowns are minimal automorphic. A key lemma to exclude certain retracts can also be applied to ordered sets recently presented in Schröder (Order, https://doi.org/10.1007/s11083-021-09574-3, 2021).

In this paper, we will prove some fixed point theorems for graphical contractions in complete b-metric spaces. Then, some common fixed point results for a pair of mappings in complete b-metric spaces will be deduced. Our results extend some recent theorems proved in classical metric spaces.

This article proposes two regularized iterative algorithms for solving variational inequality problems defined over a solution set of a variational inclusion problem, known as hierarchical variational inequality problems, in the setting of Hadamard manifolds. Instead of regularizing the variational inequality problem or an iterative method for solving it, we first regularize the considered variational inclusion problem, and then prove that the solution of the regularized problem converges to a solution of the hierarchical variational inequality problem. Using such a result, we prove the convergence of the sequences generated by the proposed algorithms to a solution of the considered hierarchical variational inequality problem. A computational experiment is provided to see the validity and effectiveness of the proposed algorithms.

In this paper, we prove that any group occurs as the group of homotopy classes of self-equivalences of a none elliptic Sullivan algebra.

In this paper, approximate Noether and Lie symmetries of 2nd order for Gibbons–Maeda–Garfinkle–Horowitz–Strominger (GMGHS) charged black hole in the Einstein frame are analyzed comprehensively. To explore the approximate Noether symmetries of 2nd order, Noether symmetries of Minkowski spacetime are used which forms a 17 dimensional Lie algebra. It is observed that no new approximate Noether symmetry is obtained at 1st and 2nd order. To examine the 1st and 2nd order approximate Lie symmetries of the GMGHS black hole spacetime, 35 Lie symmetries (exact) of the Minkowski spacetime are used which forms an algebra sl(6, R). It is shown that no new approximate Lie symmetry exists at 1st and 2nd order and only exact 35 symmetries are recouped as trivial approximate Lie symmetries at both orders. Furthermore, no energy rescaling factor is seen in this spacetime.

We show that for each (nge 2in {mathbb {N}}), the varieties ({mathbb {V}}_{n}=[x_1x_2x_3=x_1^nx_{i_1}x_{i_2}x_{i_3}]) where i is any non-trivial permutation of ({1,2,3}) are closed. Further, we show that for each (nin {mathbb {N}}), the varieties ({mathcal {V}}_{n}=[x_1x_2x_3=x_1^nx_{i_1}x_{i_2}x_{i_3}]) where i is any non-trivial permutation of ({1,2,3}) other than the permutation (231) are closed.

The concept of (mu )-strong Cesaro summability at infinity for a locally integrable function is introduced in this work. The concept of (mu )-statistical convergence at infinity is also considered and the relationship between these two concepts is established. The concept of (mu left[ pright] )-strong convergence at infinity point, generated by the measure (mu left( cdot right) ) is also considered. Similar results are obtained in this case too. This approach is applied to the study of the convergence of the Fourier–Stieltjes transforms.

In this paper, we study the stabilization problem of a disk beam structure with disturbance. Specifically, the structure consists of a beam clamped at one end to the center of a rotating rigid disk, while the other end is attached to a tip mass subject to a non-uniform bounded disturbance. We start the investigation by designing the controller via the Active disturbance rejection control (ADRC) approach. The high gain extended state observer (ESO) is first designed to estimate the disturbance, then the feedback observer-based controller is designed to employ the estimation to cancel the disturbance effect. Furthermore, the well-posedeness of the controlled system is proved using the semigroup theory. Using the Lyapunov method, the exponential stability is proved. Finally, the performance of the control method is illustrated by simulation results.

We consider the problem of maximal regularity for the semilinear non-autonomous evolution equations

Here, the time-dependent operators A(t) are associated with (time dependent) sesquilinear forms on a Hilbert space (mathcal {H}.) We prove the maximal regularity result in temporally weighted (L^2)-spaces and other regularity properties for the solution of the previous problem under minimal regularity assumptions on the forms, the initial value (u_0) and the inhomogeneous term F. Our results are motivated by boundary value problems.