Arabian Journal of Mathematics最新文献

The spectral decomposability of a closed linear relation T on a complex Banach space is demonstrated through three new characterisations: The first two are expressed in terms of the extended Bishop and decomposition properties while the third one is given by means of the coinduced operator of T and its local spectral subspaces. This has been achieved through the intensive study of the properties of the last mentioned subspaces as well as the ER-SVEP.

In this paper, we investigate the unique solvability of a generalized Tricomi problem with an integral condition for a loaded equation involving a fractional operator. By analyzing the problem for a third-order equation with a telegraph operator, we extend the results to a generalized operator with small parameters. Furthermore, the integral condition in the parabolic region enables the generalization of local problems associated with second- and third-order equations.

For the modified Newton-type (MN) iteration method for solving the GAVE, the convergence conditions and the quasi-optimal parameter matrix are discussed. The sufficient conditions are supplied to ensure that the GAVE has a unique solution. Besides, the numerical experiments are illustrated to show some of the presented results.

Let R be a commutative Noetherian ring, and let C be a semidualizing R-module. The present paper aims at studying some properties of ({textrm{Hom}_{textrm{R}}}(C, M)) and (C otimes _{R} M) where M is a non-zero finitely generated R-module. Also, we investigate other versions of depth formula for relative Tor-independent modules with respect to C. Finally, we establish relative versions of Ischebeck and Chouinard formulas for R-modules of finite relative homological dimensions with respect to C.

The class of O-metric spaces generalizes several existing metric-type spaces in literature including metric spaces, b-metric spaces, and ultra metric spaces. In this paper, we discuss the properties of the topology induced by an O-metric and establish in the setting, fixed point theorems for contractions and generalized contractions. The proofs of the theorems rely heavily on polygon ({{textbf {o}}})-inequalities which are a natural generalization of the triangle inequality, and the construction of which leads to the notion of ({{textbf {o}}})-series following a pattern of functions. As application, conditions for the existence of solutions of initial value problems are discussed and a generalization of Lebesgue spaces is introduced.

This research introduces an innovative algorithmic framework tailored to solve the inverse boundary data completion problem for time-fractional diffusion equations in a bounded domain, especially under partially specified Neumann and Dirichlet conditions. This issue is notoriously ill-posed in the Hadamard sense, which demands a sophisticated and nuanced approach. Our method innovatively transforms this problem into a system of first-order differential equations linked with Matrix Riccati Differential Equations. Moving beyond traditional methods, our framework integrates a state-of-the-art decoupling algorithm, which effectively blends the strategic depth of optimal control theory with the precision of the Golden Section Search algorithm. This integration determines the optimal regularization parameter essential for ensuring the stability and the reliability of the solution. The robustness and effectiveness of our approach have been rigorously verified through extensive numerical experiments, proving its resilience even in conditions marked by significant noise levels.

In this article, we discuss the category (mathcal{S}mathcal{N}_2) where the objects are finite-dimensional nilpotent Lie superalgebras of class two and the category (mathcal {SSKE}) where the objects are skew-supersymmetric bilinear maps. We establish a relation between (mathcal{S}mathcal{N}_2) and (mathcal {SSKE}). As a result, we discuss the capability of nilpotent Lie superalgebras of class two.

The mainspring of this analytical study is to implement the idea of delayed argument cosine and sine conformable matrices to interpret the stability bounds of conformable type fractional operator over finite time period using modified integral form of Gronwall’s inequality. Further, we establish the conformable Grammian matrices in-terms of sine function to analyze the controllability results. The main inception is to first consider the linear controllability result of our defined system and to a greater extent, fixed point techniques along with the properties of Bochner-integral and inner product spaces are implemented to verify the controllability results of the nonlinear system. The theoretical study is graphically visualized using matlab software.

A new analogue of the nonlinear Lupaş type Bernstein operators using max-product algebra and q-integers, which possess the endpoint interpolation property, is constructed. Quasi-convexity, monotonicity, and shape-preserving properties are studied. The graphs have also been added to support the theoretical results.

Recent advances have introduced derivative-free projection methods incorporating a relaxed-inertial technique to solve large-scale systems of nonlinear equations (LSoNE). These methods are often studied under restrictive assumptions such as monotonicity and Lipschitz continuity assumptions. In this paper, we propose a new class of derivative-free projection method with a relaxed inertial technique for solving LSoNE. Unlike existing approaches that rely on monotonicity and Lipschitz continuity assumptions, our method extends beyond these limitations, broadening the applicability of projection methods to more general problem classes. This enhances both the theoretical framework and the practical efficiency in large-scale applications. Moreover, we establish global convergence without the need for a summability condition on the inertial extrapolation step length. To demonstrate the effectiveness of the method, we present numerical experiments to solve LSoNE and regularized decentralized logistic regression, a key problem in machine learning applications.