Sandoval-Hernandez, Mario A. Vazquez-Leal, Hector Filobello-Nino, Uriel Hernandez-Martinez, Luis
Published in
Open Mathematics

In this work, we propose to approximate the Gaussian integral, the error function and the cumulative distribution function by using the power series extender method (PSEM). The approximations proposed in this paper present a high accuracy for the complete domain [–∞,∞]. Furthermore, the approximations are handy and easy computable, avoiding the app...

Zhang, Qinghua Zhu, Yueping
Published in
Open Mathematics

This paper investigates the abstract-valued Orlicz space of range-varying type. We firstly give the notions and examples of partially continuous modular net and regular Banach space net of type (II), then deal with the definitions, constructions, and geometrical properties of the range-varying Orlicz spaces, including representation of the dual L+φ...

Wang, Hongjuan
Published in
Open Mathematics

In this paper we investigate theoretically and numerically the new preconditioned method to accelerate over-relaxation (AOR) and succesive over-relaxation (SOR) schemes, which are used to the large sparse linear systems. The iterative method that is usually measured by the convergence rate is an important method for solving large linear equations, ...

El-Sayed, Ahmed M. A. Abd El-Salam, Sheren A.
Published in
Open Mathematics

Here, a coupled system of nonlinear weighted Cauchy-type problem of a diffre-integral equations of fractional order will be considered. We study the existence of at least one integrable solution of this system by using Schauder fixed point Theorem. The continuous dependence of the uniqueness of the solution is proved.

Bakery, Awad A. Mohammed, Mustafa M.
Published in
Open Mathematics

Let E be a generalized Cesáro sequence space defined by weighted means and by using s-numbers of operators from a Banach space X into a Banach space Y. We give the sufficient (not necessary) conditions on E such that the components SE(X,Y):={T∈L(X,Y):((sn(T))n=0∞∈E}, $$\begin{array}{} \displaystyle S_{E}(X, Y):=\Big\{T\in L(X, Y):((s_{n}(T))_{n=0}^...

Alhojilan, Yazid
Published in
Open Mathematics

This paper aims to present a new pathwise approximation method, which gives approximate solutions of order 32 $\begin{array}{} \displaystyle \frac{3}{2} \end{array}$ for stochastic differential equations (SDEs) driven by multidimensional Brownian motions. The new method, which assumes the diffusion matrix non-degeneracy, employs the Runge-Kutta met...

Luo, Shuzhen Xu, Xiaoquan
Published in
Open Mathematics

In this paper, the concepts of weak quasi-hypercontinuous posets and weak generalized finitely regular relations are introduced. The main results are: (1) when a binary relation ρ : X ⇀ Y satisfies a certain condition, ρ is weak generalized finitely regular if and only if (φρ(X, Y), ⊆) is a weak quasi-hypercontinuous poset if and only if the interv...

Hou, Zhiwu Jing, Xia Gao, Lei
Published in
Open Mathematics

A new error bound for the linear complementarity problem (LCP) of Σ-SDD matrices is given, which depends only on the entries of the involved matrices. Numerical examples are given to show that the new bound is better than that provided by García-Esnaola and Peña [Linear Algebra Appl., 2013, 438, 1339–1446] in some cases. Based on the obtained resul...

Nazam, Muhammad Arshad, Muhammad Park, Choonkil Mahmood, Hasan
Published in
Open Mathematics

The purpose of this paper is to study behavior of a rational type contraction introduced in [A fixed point theorem for contractions of rational type in partially ordered metric spaces, Ann. Univ. Ferrara, 2013, 59, 251–258] in context of ordered dualistic partial metric spaces and to investigate sufficient conditions for the existence of a fixed po...

Zennir, Khaled
Published in
Open Mathematics

In this paper we consider a class of nD Navier-Stokes equations of Kirchhoff type and prove the global existence of solutions by using a new approach introduced in [Jday R., Zennir Kh., Georgiev S.G., Existence and smoothness for new class of n-dimentional Navier-Stokes equations, Rocky Mountain J. Math., 2019, 49(5), 1595–1615].