A novel local meshless scheme based on the radial basis function (RBF) is introduced in this article for price multi-asset options of even European and American types based on the Black-Scholes model. The proposed approach is obtained by using operator splitting and repeating the schemes of Richardson extrapolation in the time direction and coupling the RBF technology with a finite-difference (FD) method that leads to extremely sparse matrices in the spatial direction. Therefore, it is free of the ill-conditioned difficulties that are typical of the standard RBF approximation. We have used a strong iterative idea named the stabilized Bi-conjugate gradient process (BiCGSTAB) to solve highly sparse systems raised by the new approach. Moreover, based on a review performed in the current study, the presented scheme is unconditionally stable in the case of independent assets when spatial discretization nodes are equispaced. As seen in numerical experiments, it has a low computational cost and generates higher accuracy. Finally, the proposed local RBF scheme is very versatile so that it can be used easily for solving numerous models and obstacles not just in the finance sector, as well as in other fields of engineering and science.

Let A and B be standard operator algebras on Banach spaces X and Y, respectively. Let ϕ, : A →,B be a bijective map. In this paper, we show that ϕ,is completely Preserving quadratic operator in both directions if and only if ϕ,is 2-quadratic Preserving operator in both directions and if and only if ϕ,is either an isomorphism or (in the complex case) a conjugate isomorphism.

The aim of this work is to characterize all bounded linear operators $T:\lpi\rightarrow\lpi$ which preserve disjoint support property. We show that the constant coefficients of all isometries on $\lpi$ are in the class of such operators, where $2\neq p\in [1,\infty )$ and $I$ is a non-empty set. We extend Preserving disjoint support property to linear operators on $\mathfrak{c}_{0}(I).$ At the end, we obtain some equivalent properties of isometries on Banach spaces.

Given an integer n≥2, in this article we provide a complete description of all additive surjective maps on the algebra of all bounded linear operators acting on an infinite-dimensional complex Banach space, Preserving in both directions the set of Drazin invertible operators of index n.

This paper focuses on investigating the equivalence problem for fifth-order differential operators (FODOs) on the line under general fiber-Preserving transformations. Utilizing the Cartan method of equivalence, the study specifically addresses the gauge equivalence problem, seeking to establish the conditions for two FODOs to be related by a fiber-Preserving transformation. By analyzing the properties of these operators, the research aims to identify conditions for their transformation while maintaining the fiber structure. The systematic approach of the Cartan method is employed to derive the necessary conditions for gauge equivalence between these FODOs. The study aims to enhance understanding of the equivalence problem for FODOs and shed light on fiber-Preserving transformations that uphold gauge equivalence.