This paper proposes a novel iterative method for addressing the split general system of variational inequalities and related fixed point problems within the framework of real Hilbert spaces. The algorithm is constructed by combining Halpern-type iterations with nonexpansive mappings, and its design guarantees strong convergence under appropriate conditions. The analytical results demonstrate that the proposed method not only unifies but also generalizes several classical schemes, including the split feasibility problem and the split variational inequality problem. To substantiate the theoretical findings, numerical experiments are provided, illustrating the robustness and efficiency of the algorithm in solving complex optimization and equilibrium problems.
Fractional-order neutral-type recurrent neural networks (FONTRNNs) hold promise for dynamic modeling, yet fixed neutral term order in existing studies restricts regulation flexibility. This paper proposes a four-neuron FONTRNN with independently tunable neutral term order. By decoupling the characteristic equation into trigonometric-variable linear systems, we derive explicit delay-dependent stability criteria and Hopf bifurcation points via Cramer's rule. Notably, an extended bifurcation framework is developed by treating the neutral term order as the bifurcation parameter, with critical values solved through implicit function curve intersection. Numerical simulations verify that reducing the derivative order consistently stabilizes the system, while adjusting the neutral term order enhances or weakens stability depending on parameter configurations.
In this paper, we define a new class of system of additive-quadratic functional equations on Banach algebras, which we call the system of i-mappings, where i is an element of {1, 2}. We introduce the notion of a i-F-homomorphism-derivations (abbreviated i-F-hom-ders), with i is an element of {1,2} : for i = 1, F is a linear homomorphism, and for i = 2, f is a quadratic homomorphism on Banach algebras. Finally, using a fixed-point method, we investigate Hyers-Ulam stability for the system of additive-quadratic functional equations and i-F-hom-ders, employing Gavruta-type, Rassias-type and JMRassias-type control functions on Banach algebras.
In this paper, we present a new second-order finite difference scheme for Riesz spacefractional Allen-Cahn equations. We use a modified Crank-Nicolson finite difference scheme with stabilized terms of third-order numerical accuracy for temporal discretization. The discrete maximum bound principle, the maximum-norm error estimates, and the discrete energy stability of the proposed scheme are discussed. It is demonstrated that the proposed scheme is maximum bound principle preserving and unconditionally energy-stable for any nonnegative stabilization parameter beta which satisfies 0 <= beta <= 1/4. As far as we know, the proposed fully implicit second-order scheme has never been proved to preserve the maximum bound principle before except the Allen-Cahn equation with beta = 1/12 and beta = 0. Finally, some numerical experiments are performed to verify the theoretical results.
This paper outlines multiple sufficient conditions for the existence of at least one generalized solution to a mixed boundary value problem for a complete Sturm-Liouville equation. Our method relies on variational techniques. We extend and enhance some recent results and also provide a specific example to illustrate an application.
