abbasali shokri

A new two-step implicit P-stable Obrechkoff of twelfth algebraic order with vanished phase-lag and its first, second and third derivatives is constructed in this paper. The purpose of this paper is to develop an efficient algorithm for the approximate solution of the second order iniitial value problems that have oscillatory or periodic solutions. This algorithm belongs in the category of the multistep and multiderivative methods. The advantage of the new methods in comparison with similar methods, in terms of efficiency, accuracy and stability, have been showed by the implementation of them in some important problems, including the undamped Duffing equation, etc. -------------- A new two-step implicit P-stable Obrechkoff of twelfth algebraic order with vanished phase-lag and its first, second and third derivatives is constructed in this paper. The purpose of this paper is to develop an efficient algorithm for the approximate solution of the second order iniitial value problems that have oscillatory or periodic solutions. This algorithm belongs in the category of the multistep and multiderivative methods. The advantage of the new methods in comparison with similar methods, in terms of efficiency, accuracy and stability, have been showed by the implementation of them in some important problems, including the undamped Duffing equation, etc.

Let X be a compact metric space with at least two elements, B be a unital commutative Banach algebra over the scalar field F=R or C, and α in R with 0<α≤1. Suppose that C(X,B) be the continuous, A(X,B) be the analytic, and Lipα(X,B) be the α-Lipschitz B-valued operator algebras on X. In this paper, we prove that the algebras Lip α(X,B) and A(X,B) are dense in C(X,B) under sup-norm. Also, we study the relationship between elements of the algebras Lip α(X,B) and A(X,B).

The Lipschitz function algebras were first defined in the 1960s by some mathematicians, including Schubert. Initially, the Lipschitz real-value and complex-value functions are defined and quantitative properties of these algebras are investigated. Over time these algebras have been studied and generalized by many mathematicians such as Cao, Zhang, Xu, Weaver, and others. Let  be a non-empty compact metric space and  be a unital commutative Banach space over the scalar field , and . In this paper, we first introduce the Banach algebras of vector-valued (B-valued) -Lipschitz operators on ,  and , then we study the point derivations on them. In the main results of this paper, we prove that all continuous point derivatives on  are zero, and at any non-isolated point X, there is a non-zero continuous point derivation on .

Let (X,d) be an infinite compact metric space, let (B,∥.∥) be a unital Banach space, and take α∈(0,1). In this work, at first we define the big and little α -Lipschitz vector-valued (B-valued) operator algebras, and consider the little α -lipschitz B -valued operator algebra, lip α (X,B) . Then we characterize its second dual space.