Temat: convergence point - Katalog OPAC zbiorów

Skocz do pozycji: 1.

Tytuł:: More on the behaviors of fixed points sets of multifunction and applications
Autorzy:: Alleche, B.
Nachi, K.
Powiązania:: https://bibliotekanauki.pl/articles/952787.pdf
Data publikacji:: 2015
Wydawca:: Akademia Górniczo-Hutnicza im. Stanisława Staszica w Krakowie. Wydawnictwo AGH
Tematy:: multifunction
fixed point
Pompeiu-Hausdorff metric
bounded proximal convergence
differential inclusion
Opis:: In this paper, we study the behaviors of fixed points sets of non necessarily pseudo-contractive multifunctions. Rather than comparing the images of the involved multifunctions, we make use of some conditions on the fixed points sets to establish general results on their stability and continuous dependence. We illustrate our results by applications to differential inclusions and give stability results of fixed points sets of non necessarily pseudo-contractive multifunctions with respect to the bounded proximal convergence.
Źródło:: Opuscula Mathematica; 2015, 35, 4; 427-443
1232-9274
2300-6919
Pojawia się w:: Opuscula Mathematica
Dostawca treści:: Biblioteka Nauki

Artykuł

Skocz do pozycji: 2.

Tytuł:: Strong convergence of implicit iteration processes for nonexpansive semigroups in Banach spaces
Autorzy:: Kozlowski, W.M.
Powiązania:: https://bibliotekanauki.pl/articles/746461.pdf
Data publikacji:: 2014
Wydawca:: Polskie Towarzystwo Matematyczne
Tematy:: fixed point
nonexpansive mapping
nonexpansive semigroup
fixed point iteration process
implicit iterative process
strong convergence
uniformly convex Banach space
Opis:: Let $C$ be a convex compact subset of a uniformly convex Banach space. Let $\{T_t\}_{t \geq0}$ be a strongly-continuous nonexpansive semigroup on $C$. Consider the iterative process defined by the sequence of equations $$x_{k+1} =c_k T_{t_{k+1}}(x_{k+1})+(1-c_k)x_k.$$ We prove that, under certain conditions on $\{c_k\}$ and $\{t_k\}$, the sequence $\{x_k\}_{n=1}^\infty$ converges strongly to a common fixed point of the semigroup $\{T_t\}_{t \geq0}$. There are known results on convergence of such iterative processes for nonexpansive semigroups in Hilbert spaces and Banach spaces with the Opial property, and also weak convergence results in Banach spaces that are simultaneously uniformly convex and uniformly smooth. In this paper, we do not assume the Opial property or uniform smoothness of the norm.
Źródło:: Commentationes Mathematicae; 2014, 54, 2
0373-8299
Pojawia się w:: Commentationes Mathematicae
Dostawca treści:: Biblioteka Nauki

Artykuł

Skocz do pozycji: 3.

Tytuł:: A new convexity property that implies a fixed point property for $L_{1}$
Autorzy:: Lennard, Chris
Powiązania:: https://bibliotekanauki.pl/articles/1293465.pdf
Data publikacji:: 1991
Wydawca:: Polska Akademia Nauk. Instytut Matematyczny PAN
Tematy:: uniform Kadec-Klee property
convergence in measure compact sets
convex sets
normal structure
Lebesgue function spaces
fixed point
nonexpansive mapping
Chebyshev centre
Opis:: In this paper we prove a new convexity property for L₁ that resembles uniform convexity. We then develop a general theory that leads from the convexity property through normal structure to a fixed point property, via a theorem of Kirk. Applying this theory to L₁, we get the following type of normal structure: any convex subset of L₁ of positive diameter that is compact for the topology of convergence locally in measure, must have a radius that is smaller than its diameter. Indeed, a stronger result holds. The Chebyshev centre of any norm bounded, convergence locally in measure compact subset of L₁ must be norm compact. Immediately from normal structure, we get a new proof of a fixed point theorem for L₁ due to Lami Dozo and Turpin.
Źródło:: Studia Mathematica; 1991, 100, 2; 95-108
0039-3223
Pojawia się w:: Studia Mathematica
Dostawca treści:: Biblioteka Nauki

Artykuł

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