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On unrestricted products of (W) contractions

100%

Bartoszek W. K.

Colloquium Mathematicum

2000

tom 86

nr 2

163-170

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.

A generalization of the Opial's theorem

75%

Cegielski A.

2007

tom Vol. 36, no 3

601-610

Opial presented in 1967 a theorem, which can be applied in order to prove the weak convergence of sequences (xk) in a Hilbert space, generated by iterative schemes of the form xk+1= Uxk for a nonexpansive and asymptotically regular operator U with nonempty Fix U. Several iterative schemes have, however, the form xk+i1 = UkXk, where (Uk) is a sequence of operators with a common fixed point. We show that under some conditions on the sequence (Uk) the sequence (xk) converges weakly to a common fixed point of operators Uk- We show also that the Opial's theorem and the Krasnoselskii-Mann theorem are the corollaries descending from the obtained results. Finally, we present some applications of the results to the convex feasibility problems.

A note on the weak convergence of a sequence of successive approximations

75%

Kalinde A. , Mishra S. , Singh S.

2006

tom Vol. 39, nr 3

619-624

In this paper we discuss the weak convergence of the sequence of successive approximations for a generalized para-nonexpansive mapping in a reflexive Banach space that satisfies Opial's condition.

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

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.

Discrete limit theorems for general Dirichlet series. III

75%

Laurinčikas A. , Macaitienė R.

Open Mathematics

2004

tom 2

nr 3

339-361

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.

Multivariable regular variation of functions and measures

63%

Meerschaert M. M. , Scheffler H.-P.

1999

tom Vol. 5, nr 1

125-146

Regular variation is an asymptotic property of functions and measures. The one variable theory is well-established, and has found numerous applications in both pure and applied mathematics. In this paper we present several new results on mul-tivariable regular variation for functions and measures.

Limit theorems for the Estermann zeta-function. II

63%

Laurinčikas A.

Open Mathematics

2005

tom 3

nr 4

580-590

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.

Resolvent Flows for Convex Functionals and p-Harmonic Maps

44%

Kuwae K.

Analysis and Geometry in Metric Spaces

2015

tom 3

nr 1

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.