Arabian Journal of Mathematics最新文献

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.

We investigate and characterize several kinds of elements such as units, idempotents, von Neumann regular, (pi )-regular and clean elements for skew PBW extensions over weak compatible rings. We also study the notions of Gelfand and Harmonic rings for these families of algebras. The results presented here extend those corresponding in the literature for commutative and noncommutative rings of polynomial type.

We aim to introduce the concept of centrally-extended left derivations and prove some related results to this new concept. The first part is devoted to prove that a centrally extended left derivation preserves the center of semiprime rings. The second part deals with equivalence between left derivations and our new concept. Finally we provide some results regarding commutativity.

Kim (Ramanujan Math Soc Lect Notes Ser 14:157–163, 2010) introduced the overcubic partition function (overline{a}(n)), which represents the number of all the overlined versions of the cubic partition counted by a(n). Let ( overline{b}_r(n)) denote the number of overcubic partitions of n with r-tuples. Several authors established many particular and infinite families of congruences for ( overline{b}_2(n)). In this paper, we show that ( overline{b}_{2^beta m+t}(n)equiv overline{b}_{t}(n) ,(mod ,2^{beta +1}), ) where (beta ge 1), (mge 0), and (tge 1) are integers. We also prove some new congruences modulo 8, 16 and 32 for (overline{b}_{4m+2}(n)), (overline{b}_{4m+3}(n)), (overline{b}_{8m+2}(n)), (overline{b}_{8m+4}(n)) and (overline{b}_{16m+4}(n)), where m is any non-negative integer.

In this paper, we present novel transcendence results for the certain Rosen continued fractions by using the Subspace Theorem.

In this paper, we investigate the highly dispersive perturbed nonlinear Schrödinger equation (NLSE) with (beta )-fractional derivatives, generalized nonlocal laws and sextic-power law refractive index. This equation is crucial for modeling complex phenomena in nonlinear optics, such as soliton formation, light pulse propagation in optical fibers, and light wave control, with potential applications in designing efficient optical communication devices. Furthermore, it provides a framework for understanding the intricate interactions between high dispersion, nonlocality, and complex nonlinearity, contributing to the development of new theories in wave physics. To accomplish this, we use the modified extended direct algebraic method. A variety of distinct traveling wave solutions are furnished. The obtained solutions comprise dark, bright, combo bright-dark and singular soliton solutions. Additionally, singular periodic solutions, rational and exponential solutions. Furthermore, graphical simulations are presented that highlight the distinctive characteristics of these solutions. Compared to Nofal et al. (Optik 228:166120, 2021), the proposed technique produced novel and diversified results. The results showcase the significant influence of fractional derivatives in shaping the characteristics of the soliton solutions, which is crucial for accurately modeling the dispersive and nonlocal effects in optical fibers. The extracted solutions confirmed the efficacy and strength of the current approach. The parameter constraints ensure the existence of the obtained soliton solutions. It is worth noting that the proposed method, being effective, consistent, and influential, can be applied to solve various other physical models and related disciplines.

In the present article, we introduce a novel generalization of modified Bernstein operators which is again a positive linear operator. We show the necessary and sufficient condition for the convergence of these operators. We also study some other approximation properties of these operators using standard tools of approximation theory.