Arabian Journal of Mathematics最新文献

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.

The main aim of this paper is to state nonexpansive Maia type fixed point theorems for Ćirić–Prešić operators in normed spaces endowed with a partial order. For this we do a thorough analysis in the hypotheses of our theorems, considering different properties of completeness, compactness, convexity and bounding. We state Maia type fixed point theorems for contraction and nonexpansive Ćirić–Prešić operators, including those defined by a multiply metric function. Fixed point theorems in spaces without a partial order, as well as, corollaries for monotone nonexpansive mappings are stated too. Our theorems generalize and improve results given by Ćirić and Prešić’s (Acta Math Univ Comenian (NS) 76:143–147, 2007) and Balazs (Mathematica 10:18–31, 2018) and extend them to nonexpansive operators.

This paper studies the existence and uniqueness of solution for the fractional Hall-magnetohydrodynamics system (HMH) and with two stochastic terms (SHMH). Based on the theory of Besov–Morrey spaces and the contraction principle, we will demonstrate tow main result. The first result shows the existence, uniqueness and the analyticity of solution for (HMH) in Besov–Morrey spaces (textrm{N}_{p,lambda }^{s}). The second result prove the existence and uniqueness of solution for (SHMH) in ({mathcal {L}}_0^1big (Omega times (0,T),{mathcal {P}};{mathcal {M}}_p^lambda big ) cap textrm{N}_{p,lambda }^{s}).

This paper proposes a nonparametric estimation of the cumulative distribution function of bivariate bounded data using the Birnbaum–Saunders kernel. We obtain its asymptotic properties and conduct a numerical study. The results demonstrate the superiority of the proposed estimator over the empirical distribution function and ordinary kernel estimator. We use the proposed estimator to analyse a real data set.