Abstract This paper focuses on second-order differential equations involving causal operators with nonlinear two-point boundary conditions. By applying the monotone iterative technique in presence of upper and lower solutions, a new comparison theorem, we obtain existence extremal solutions. is an extension classical theory equations. Finally, present two examples to show usefulness our results.

‎In a real Hilbert space‎, ‎an iterative scheme is considered to‎ ‎obtain strong convergence which is an essential tool to find a‎ ‎common fixed point for a countable family of nonexpansive mappings‎ ‎and the solution of a variational inequality problem governed by a‎ ‎monotone mapping‎. ‎In this paper‎, ‎we give a procedure which results‎ ‎in developing Shehu's result to solve equilibrium prob...

In this paper, we solve the MOSFET RF circuit ordinary differential equations with the waveform relaxation method, monotone iterative method, and Runge-Kutta method. With the monotone iterative method, we prove each decoupled and transformed circuit equation converges monotonically. This method provides an alternative in the time domain numerical solution of MOSFET RF circuit equations.

Strongly Fejér monotone mappings are widely used to solve convex problems by corresponding iterative methods. Here the maximal of such mappings with respect to set inclusion of the images are investigated. These mappings supply restriction zones for the successors of Fejér monotone iterative methods. The basic tool is the representation of the images by intersection of certain balls.

Ahsrract -A new design technique for linear-phase FIR filters, based on maximally flat building blocks, is presented. The design technique does not involve iterative approximations and is, therefore, fast. It gives rise to filters that have a monotone stopband response, as required in some applications. The technique is partially based on an interpolative scheme. Implementation of the obtained ...

Two-stage parallel Newton iterative methods to solve nonlinear systems of the form F (x) = 0 are introduced. These algorithms are based on the multisplitting technique and on the two-stage iterative methods. Convergence properties of these methods are studied when the Jacobian matrix F ′(x) is either monotone or an H-matrix. Furthermore, in order to illustrate the performance of the algorithms ...

*Correspondence: [email protected] 2Department of Information Engineering, Guangdong Medical College, Dongguan, Guangdong 523808, China Full list of author information is available at the end of the article Abstract In this paper, we study the existence of positive solutions for a nonlinear fractional boundary value problem on the half-line. Based on the monotone iterative technique, we obtain the...

The principal goal of this work is to investigate new sufficient conditions for the existence and convergence positive definite solutions certain classes matrix equations. Under specific assumptions, basic tool in our study a monotone mapping, which admits unique fixed point setting partially ordered Banach space. To estimate these equations, we use Krasnosel’skiĭ iterative technique. We also d...