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1
Content available remote

On unrestricted products of (W) contractions

100%
Bartoszek W. K.
Colloquium Mathematicum
|
2000
|
tom 86
|
nr 2
163-170
EN
Given a family of (W) contractions $T_1, ..., T_N$ on a reflexive Banach space X we discuss unrestricted sequences $T_{r_n}∘...∘T_{r_1}(x)$. We show that they converge weakly to a common fixed point, which depends only on x and not on the order of the operators $T_{r_n}$ if and only if the weak operator closed semigroups generated by $T_1, ..., T_N$ are right amenable.
2
Content available remote

Discrete limit theorems for general Dirichlet series. III

75%
Laurinčikas A., Macaitienė R.
Open Mathematics
|
2004
|
tom 2
|
nr 3
339-361
EN
Here we prove a limit theorem in the sense of the weak convergence of probability measures in the space of meromorphic functions for a general Dirichlet series. The explicit form of the limit measure in this theorem is given.
3
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Local convergence of inexact Newton methods under affine invariant conditions and hypotheses on the second Fréchet derivative

75%
Argyros I. K.
Applicationes Mathematicae
|
1999
|
tom 26
|
nr 4
457-465
EN
We use inexact Newton iterates to approximate a solution of a nonlinear equation in a Banach space. Solving a nonlinear equation using Newton iterates at each stage is very expensive in general. That is why we consider inexact Newton methods, where the Newton equations are solved only approximately, and in some unspecified manner. In earlier works [2], [3], natural assumptions under which the forcing sequences are uniformly less than one were given based on the second Fréchet derivative of the operator involved. This approach showed that the upper error bounds on the distances involved are smaller compared with the corresponding ones using hypotheses on the first Fréchet derivative. However, the conditions on the forcing sequences were not given in affine invariant form. The advantages of using conditions given in affine invariant form were explained in [3], [10]. Here we reproduce all the results obtained in [3] but using affine invariant conditions.
4
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Limit theorems for the Estermann zeta-function. II

63%
Laurinčikas A.
Open Mathematics
|
2005
|
tom 3
|
nr 4
580-590
EN
A limit theorem in the sense of the weak convergence of probability measures in the space of meromorphic functions for the Estermann zeta-function is obtained.
5
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Resolvent Flows for Convex Functionals and p-Harmonic Maps

45%
Kuwae K.
Analysis and Geometry in Metric Spaces
|
2015
|
tom 3
|
nr 1
EN
We prove the unique existence of the (non-linear) resolvent associated to a coercive proper lower semicontinuous function satisfying a weak notion of p-uniform λ-convexity on a complete metric space, and establish the existence of the minimizer of such functions as the large time limit of the resolvents, which generalizing pioneering work by Jost for convex functionals on complete CAT(0)-spaces. The results can be applied to Lp-Wasserstein space over complete p-uniformly convex spaces. As an application, we solve an initial boundary value problem for p-harmonic maps into CAT(0)-spaces in terms of Cheeger type p-Sobolev spaces.
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