In this paper, we design some iterative schemes for solving operator equation $ Lu=f $, where $ L:Hrightarrow H $ is a bounded, invertible and self-adjoint operator on a separable Hilbert space $ H $. In this concern,  Richardson and Chebyshev iterative methods are two outstanding as well as long-standing ones. They can be implemented in different ways via different concepts.In this paper...

The purpose of this paper is to obtain sufficient conditions for the existence of a unique fixed point of T -Kannan type mappings on complete cone metric spaces depended on another function.

It was observed in [Su5] that the spectrum of a periodic Schrodinger operator on a Riemannian manifold has band structure if the transformation group acting on the manifold satisfies the Kadison property (see below for the definition). Here band structure means that the spectrum is a union of mutually disjoint, possibly degenerate closed intervals, such that any compact subset of R meets only f...

‎Using the explicit forms of eigenstates for linearized operator related to a matrix version of Nonlinear Schrödinger equation‎, ‎soliton perturbation theory is developed for the $F=1$ bright spinor Bose-Einstein condensates‎. ‎A small disturbance of the integrability condition can be considered as a small correction to the integrable equation‎. ‎By choosing appropriate perturbation‎, ‎the soli...

Regular operators on L p-spaces are characterised in terms of an operator bound which is associated with certain generalisations of the Feynman-Kac formula. of multiplication by the characteristic functions of elements of the-algebra S, so that if f is a bounded S-measurable function, Q(f) = R f dQ is the operator of multiplication by f. When is it true that we can nd a positive number C such t...

A new continuous regularized Gauss-Newton-type method with simultaneous updates of the operator (F (x(t))F (x(t)) + ε(t)I) for solving nonlinear ill-posed equations in a Hilbert space is proposed. A convergence theorem is proved. An attractive and novel feature of the proposed method is the absence of the assumptions about the location of the spectrum of the operator F (x). The absence of such ...

where Δ is the forward difference operator Δxn = xn+1 − xn, Δxn = Δ(Δxn), φp(s) is p-Laplacian operator φp(s) = |s|p−2s (1 < p < ∞), and f : Z×R3 → R is a continuous functional in the second, the third, and fourth variables and satisfies f (t +m,u,v,w) = f (t,u,v,w) for a given positive integerm. We may think of (1.1) as being a discrete analogue of the second-order functional differential equa...

The states |α,m〉, defined as â†m|α〉 up to a normalization constant and m is a nonnegative integer, are shown to be the eigenstates of f(n̂,m)â where f(n̂,m) is a nonlinear function of the number operator n̂. The explicit form of f(n̂,m) is constructed. The eigenstates of this operator for negative values of m are introduced. The properties of these states are discussed and compared with those of th...

The Banach-Stone theorem states that any surjective, linear mapping T between spaces of continuous functions that satisfies ‖T (f)− T (g)‖ = ‖f − g‖, where ‖ · ‖ denotes the uniform norm, is a weighted composition operator. We study a multiplicative analogue, and demonstrate that a surjective mapping T , not necessarily linear, between algebras of continuous functions with ‖T (f)T (g)‖ = ‖fg‖ m...

This paper presents a review of the Gauss-Kuzmin-Wirsing (GKW) operator. The GKW operator is the transfer operator of the Gauss map, and thus has connections to the theory of continued fractions – specifically, it is the shift operator for continued fractions. The operator appears to have a reasonably smooth, well-behaved structure, however, no closed-form analytic solutions are known, and thes...