We prove an existence and uniqueness theorem for solving the operator equation F(x) + G(x)= 0, where F is a continuous and Gâteaux differentiable operator and the operator G satisfies Lipschitz condition on an open convex subset of a Banach space. As corollaries, a recent theorem of Argyros (2003) and the classical convergence theorem for modified Newton iterates are deduced. We further obtain ...

In this paper we give a thoughtful exposition of the Clifford algebra Cl(HV ) of multivecfors which is naturally associated with a hyperbolic space HV , whose elements are called vecfors. Geometrical interpretation of vecfors and multivecfors are given. Poincaré automorphism (Hodge dual operator) is introduced and several useful formulas derived. The role of a particular ideal in Cl(HV ) whose ...

A generalized anti-hermitian staggered Dirac operator is formulated. Its relation with noncommutative geometry is briefly reviewed. Once this antihermitian operator is modified to be “γ5-hermitian”, it will provide a new solution to Ginsparg-Wilson relation, basing on an abstract algebraic analysis of Neuberger’s overlap construction and a redefinition of chirality.

This work contributes to the domains of Boolean algebra and of Bayesian probability, by proposing an algebraic extension of Boolean algebras, which implements an operator for the Bayesian conditional inference and is closed under this operator. It is known since the work of Lewis (Lewis’ triviality) that it is not possible to construct such conditional operator within the space of events. Never...

This article is designed to provide an introduction to some examples of triangulated categories that arise in the study of G-equivariant cohomology theories for a compact Lie group G. We focus on cohomology theories whose values are rational vector spaces since one may often give explicit algebraic constructions of the triangulated category in that case. As general references for equivariant co...

This paper reviews and compares constructive and algebraic approaches in the study of rough sets. In the constructive approach, one starts from a binary relation and defines a pair of lower and upper approximation operators using the binary relation. Different classes of rough set algebras are obtained from different types of binary relations. In the algebraic approach, one defines a pair of du...

1. Abstract The main purpose of this paper is to describe a numerical method of an inverse problem for two– dimensional flow of fluid around a profile. The principle of the method is based on construction of a contractive operator. The practical use is getting the possibility of constructing or modifying the shape of a profile by the velocity distribution on the profile surface. We formulate an...

The aim of this text is the study of the fine spectra for a class of Cesàro generalized operators, Rhaly operators, when those are defined on the spaces lp, p > 1. 2000 Mathematical Subject Classification: 65F15 The averaging operators A are determined by relations inf x∈X f(x) ≤ A(f) ≤ sup x∈X f(x) , ∀ f ∈ F = {f | f : X → R}, where ∅ 6= X ⊂ R. A(f) is the mean of f for the operator A. For a =...

in this paper, we give some results on the common fixed point of self-mappings defined on complete $b$-metric spaces. our results generalize kannan and chatterjea fixed point theorems on complete $b$-metric spaces. in particular, we show that two self-mappings satisfying a contraction type inequality have a unique common fixed point. we also give some examples to illustrate the given results.

. (1.2) In the manipulations above we have used the linearity of the superoperator M in the first line. In the second line we have used Lemma 0.4 with γ = I ⊗ σ , noting that |X|= s. The third line follows from the concavity of the square root. We will now use a helpful identity for the trace of an operator squared: TrZ =Tr(Z ⊗ Z)F , where F is defined as follows. Definition 1.1. The swap opera...