Arabian Journal of Mathematics最新文献

In the paper, we investigate the uniqueness problem of a meromorphic function and its difference operator to the most general setting via two shared set problems and thus improve a recent result of Chen–Chen (Bull Malays Math Sci Soc 35(3): 765-774, 2012) .

The objective of this research is to prove that an additive mapping (Delta :{mathcal {A}}rightarrow {mathcal {A}}) will be a generalized derivation associated with a derivation (partial :{mathcal {A}}rightarrow {mathcal {A}}) if it satisfies the following identity (Delta (r^{m+n+p})=Delta (r^m)r^{n+p}+r^mpartial (r^{n})r^p+r^{m+n}partial (r^p)) for all (rin {mathcal {A}}), where (m, nge 1) and (pge 0) are fixed integers and ({mathcal {A}}) is a semiprime ring. Another analogous has been done where an additive mapping behaves like a generalized left derivation associated with a left derivation on ({mathcal {A}}) satisfying certain algebraic identity. The proofs of these advancements are derived employing algebraic concepts. These theorems have been validated by offering an example that shows they are not insignificant. Furthermore, we provide an application in the framework of Banach algebra.

In this work, we consider fractional variational problems depending on higher order fractional derivatives. We obtain optimality conditions for such problems and we present and discuss some examples. We conclude with possible research directions.

In this paper, we consider a finite family of sets (geometric constraints) (F_{1}, F_{2},ldots , F_{r}) in the Euclidean space ({mathbb {R}}^n.) We show under mild conditions on the geometric constraints that the “perturbation property” of the constrained best approximation from a nonempty closed set (K cap F) is characterized by the “convex conical hull intersection property” (CCHIP in short) at a reference feasible point in F. In this case, F is the intersection of the geometric constraints (F_{1}, F_{2},ldots , F_{r},) and K is a nonempty closed convex set in ({mathbb {R}}^n) such that (K cap F ne emptyset .) We do this by first proving a dual cone characterization of the contingent cone of the set F. Finally, we obtain the “Lagrange multiplier characterizations” of the constrained best approximation. Several examples are given to illustrate and clarify our results.

The purpose of this article is to obtain appropriate tools for solving fractional differential equations that are flexible enough to adapt to different purposes. We thus look for a very general fractional Fourier transform with a phase function which can be appropriately chosen according to the problem you want to face.

In this paper, we consider the nonlocal elliptic problem involving a mixed local and nonlocal operator,

where (Omega subset {mathbb {R}}^N) is a bounded regular domain, (mathfrak {L_{p,s}}equiv -Delta _p+(-Delta )^s_p), (0<s<1<p<N), (alpha ,,beta in {mathbb {R}}) and (f: Omega times {mathbb {R}}rightarrow {mathbb {R}}) be a nonnegative function which is defined almost everywhere with respect to the variable x. Using Schauder and Tychonoff fixed point theorems, we get two existence theorems of weak positive solutions under some hypothesis on (alpha , beta ) and f.

We focus on two-phase problems with singular and superlinear parametric terms on the right-hand side. Using fibering maps and the Nehari manifold method, we prove that there are at least two non-trivial positive solutions in a geometric setting that is locally similar to Euclidean spaces but has different global properties for all except the smallest values of parameter (mu > 0.) Singularities may appear at discrete locations in the manifold, which is a challenge for the work due to the unpredictable behavior of the solution. The findings presented here generalize some known results.

This paper attempts to prove the Lipschitz continuity of the resolvent operator associated with a ((P,eta ))-accretive mapping and compute an estimate of its Lipschitz constant. This is done under some new appropriate conditions that are imposed on the parameter and mappings involved in it; with the goal of approximating a common element of the solution set of a system of generalized variational-like inclusions and the fixed point set of a total asymptotically nonexpansive mapping in the framework of real Banach spaces. A new iterative algorithm based on the resolvent operator technique is proposed. Under suitable conditions, we prove the strong convergence of the sequence generated by our proposed iterative algorithm to a common element of the two sets mentioned above. The final section is dedicated to investigating and analyzing the notion of a generalized H(., .)-accretive mapping introduced and studied by Kazmi et al. (Appl Math Comput 217:9679–9688, 2011). In this section, we provide some comments based on the relevant results presented in their work.

In this paper, a discrete-time model of a plant–herbivore system is qualitatively analyzed using difference equations to describe population dynamics over time. The goal is to examine how the model behaves under varying parameter values and initial conditions. Results reveal that the model exhibits diverse dynamical behaviors such as stable equilibria, period-doubling cascade, and chaotic attractors. The analysis indicates that changes in crucial parameters greatly affect the system’s dynamics. This study offers crucial insights into plant–herbivore systems and highlights the value of qualitative analysis in comprehending intricate ecological systems.

The role of symmetries and first integrals are well known mechanisms for the reduction of ordinary differential equations (odes) and, used in conjunction, lead to double reductions of the odes. In this article, we attempt to construct the first integrals of a large class of the well known second-order Painlevé equations. In some cases, variational and/or gauge symmetries have additional applications following a known Lagrangian in which case the first integral is obtained by Noether’s theorem. Sometimes, it is more convenient to adopt the ‘multiplier’ approach to find the first integrals. In a number of cases, we can conclude that the class is linearizable.