It is known that a Fréchet space F can be realized as a projective limit of a sequence of Banach spaces Ei. The space Kc(F) of all compact, convex subsets of a Fréchet space, F, is realized as a projective limit of the semilinear metric spacesKc(E). Using the notion of Hukuhara derivative for maps with values inKc(F), we prove the local and global existence theorems for an initial value problem...

Given a digital curve and a maximum error, we propose an algorithm that computes a simplification of the curve such that the Fréchet distance between the original and the simplified curve is less than the error. The algorithm uses an approximation of the Fréchet distance, but a guarantee over the quality of the simplification is proved. Moreover, even if the theoretical complexity of the algori...

We present a local convergence analysis of a Modified Halley-Like Method of high convergence order in order to approximate a solution of a nonlinear equation in a Banach space. Our sufficient convergence conditions involve only hypotheses on the first Fréchet-derivative of the operator involved. Earlier studies use hypotheses up to the third Fréchet-derivative [26]. Numerical examples are also ...

in this paper, we nd the relationships between module contractibility of abanach algebra and its ideals. we also prove that module contractibility ofa banach algebra is equivalent to module contractibility of its module uniti-zation. finally, we show that when a maximal group homomorphic image ofan inverse semigroup s with the set of idempotents e is nite, the moduleprojective tensor product ...

Abstract In this paper, the concept of generalized saddle point(GSP) is employed to discuss the optimization problems of a set of convex functions on a normed linear space X , which presents an equivalence under a special condition between GSP and its optimum solution. A study on integrated convex optimization problem by using Gâteaux and Fréchet differentiability respectivly, and the equivalen...

In this paper, we study the semilocal convergence of a fifth order iterative method using recurrence relation under the assumption that first order Fréchet derivative satisfies the Hölder condition. Also, we calculate the R-order of convergence and provide some a priori error bounds. Based on this, we give existence and uniqueness region of the solution for a nonlinear Hammerstein integral equa...

As usual, we consider integral operators attached to compactly supported measures η on the group G, and exploit the intrinsic sense of such operators on any reasonable representation space for G, for example, Hilbert, Banach, Fréchet, and LF (strict colimits of Fréchet), or, generally,, quasi-complete, locally convex spaces. For a representation π, V of G, and a compactly-supported measure η, t...

We introduce the concepts of growth and spectral bound for strongly continuous semigroups acting on Fréchet spaces and show that the Banach space inequality s(A) 6 ω0(T ) extends to the new setting. Via a concrete example of an even uniformly continuous semigroup we illustrate that for Fréchet spaces effects with respect to these bounds may happen that cannot occur on a Banach space.

and Applied Analysis 3 Here, R󸀠(κ)∗R(κ) is the Fréchet derivative of the residual operatorR(κ)with respect to κ, and the forcing termpoints in the descent direction of the least squares cost; t is the artificial iteration time, and C is a conveniently chosen constant. The Fréchet derivative can be calculated efficiently using the adjoint formulation (see [9, 12]). Numerically discretizing, we a...

In this paper, we study a problem on computing the Fréchet distance between two polygonal curves and provide efficient solutions for solving it. In the classical Fréchet distance, point objects move arbitrarily fast on the polygonal curves. Here, we consider the problem instance where the speed per segment is a constant within a specified range. We first describe a naive algorithm which solves ...