Let X be a real or complex Banach space and Y be a normed linear space. Suppose that f:X → Y is a Frechet differentiable function and F:X ⇉ 2 is a set-valued mapping with closed graph. Uniform convergence of Chord method for solving generalized equation y ∈ f x + F x ...... . (∗), where y ∈ Y a parameter, is studied in the present paper. More clearly, we obtain the uniform convergence of the se...

I A more general theory will result if in the place of R we employ an abstract normed ring. s We use the symbols =, ... ... in more than one sense. No confusion need arise as tie context makes clear the meaning of each such symbol. It is worth while to mention here that the relation of equality = for E1 as well as for E2 is not an independent primitive idea; for, an equivalent set of postulates...

Received (received date) Revised (revised date) Communicated by (Name) The article analyzes similarity of closed polygonal curves in Frechet metric, which is stronger than the well-known Hausdorff metric and therefore is more appropriate in some applications. An algorithm that determines whether the Frechet distance between two closed polygonal curves with m and n vertices is less than a given ...

The notions of compact convex variation and compact convex subdifferential for the mappings from a segment into a locally convex space (LCS) are studied. In the case of an arbitrary complete LCS, each indefinite Bochner integral has compact variation and each strongly absolutely continuous and compact subdifferentiable a.e. mapping is an indefinite Bochner integral. 0. Introduction and prelimin...

The simultaneous estimation of coefficients and the initial conditions for model fractional parabolic systems porous media is reduced to minimization a least-squares cost functional. This inverse problem uses information about pressures at finite number space time points. Frechet gradient functional derived. application conjugate method numerical parameter also discussed. Computational results ...

It was shown in papers of Dosi and a recent article the author that there is sheaf Frechet-Arens-Michael algebras (locally solvable complex case polynomial growth real) on character space nilpotent Lie algebra. For algebra group affine transformations line (the simplest non-nilpotent algebra) we construct analogous sheaves non-commutative smooth holomorphic functions special set representations.

It is shown that the initial value problem (IVP) of the generalized KdV equation @tu + @x(a(u)) + @ 3 xu = 0; u(x; 0) = (x) is well posed in the classical Sobolev space H(R) with s > 3=4, which thus establishes a nonlinear map K from H(R) to C([ T; T ];H(R)). Then it is proved that (i) if a = a(x) is a C function on R to R, then K is in nitely many times Frechet di erentiable; (ii) if a = a(x) ...

For a hyperbolic type model equation of third order a Darboux type problem is investigated in a dihedral angle. It is shown that there exists a real number ρ0 such that for α > ρ0 the problem under consideration is uniquely solvable in the Frechet space. In the case where the coefficients are constants, Bochner’s method is developed in multidimensional domains, and used to prove the uniquely so...

The modification of the Clarke generalized subdiNerentia1 due to Michel and Penot is a useful tool in determining differentiability properties for certain classes of real functions on a normed linear space. The Glteaux differentiability of any real function can be deduced from the GBteaux differentiability of the norm if the function has a directional derivative which attains a constant related...

Given a compact Kahler manifold, the space $\mathcal H$ of its (relative) potentials is an infinite dimensional Frechet on which Mabuchi and Semmes have introduced natural connection $\nabla$. We study certain Lagrangians $T\mathcal H$, in particular Finsler metrics, that are parallel with respect to connection. show geodesics $\nabla$ paths least action, prove convexity property action. This g...