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    Wyświetlanie 1-14 z 14
    Tytuł:
    Hyperconvexity of ℝ-trees
    Autorzy:
    Kirk, W.
    Powiązania:
    https://bibliotekanauki.pl/articles/1205371.pdf
    Data publikacji:
    1998
    Wydawca:
    Polska Akademia Nauk. Instytut Matematyczny PAN
    Tematy:
    hyperconvex metric space
    ℝ-tree
    fixed point
    nonexpansive mapping
    Opis:
    It is shown that for a metric space (M,d) the following are equivalent: (i) M is a complete ℝ-tree; (ii) M is hyperconvex and has unique metric segments.
    Źródło:
    Fundamenta Mathematicae; 1998, 156, 1; 67-72
    0016-2736
    Pojawia się w:
    Fundamenta Mathematicae
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    Convergence of iterates of asymptotically nonexpansive mappings in Banach spaces with the uniform Opial property
    Autorzy:
    Bruck, Ronald
    Kuczumow, Tadeusz
    Reich, Simeon
    Powiązania:
    https://bibliotekanauki.pl/articles/967351.pdf
    Data publikacji:
    1993
    Wydawca:
    Polska Akademia Nauk. Instytut Matematyczny PAN
    Tematy:
    convergence of iterates
    uniform Opial property
    asymptotically nonexpansive mapping
    Źródło:
    Colloquium Mathematicum; 1993, 65, 2; 169-179
    0010-1354
    Pojawia się w:
    Colloquium Mathematicum
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    Strong convergence theorem of a hybrid projection algorithm for a family of quasi-φ-asymptotically nonexpansive mappings
    Autorzy:
    Tang, J. F.
    Chang, S. S.
    Liu, M.
    Liu, J. A.
    Powiązania:
    https://bibliotekanauki.pl/articles/255543.pdf
    Data publikacji:
    2010
    Wydawca:
    Akademia Górniczo-Hutnicza im. Stanisława Staszica w Krakowie. Wydawnictwo AGH
    Tematy:
    quasi-phi-asymptotically nonexpansive mapping
    asymptotically regular mapping
    hybrid projection iterative algorithm
    strong convergence theorem
    Opis:
    The main purpose of this paper is by using a new hybrid projection iterative algorithm to prove some strong convergence theorems for a family of quasi-φ-asymptotically nonexpansive mappings. The results presented in the paper improve and extend the corresponding results announced by some authors.
    Źródło:
    Opuscula Mathematica; 2010, 30, 3; 341-348
    1232-9274
    2300-6919
    Pojawia się w:
    Opuscula Mathematica
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    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
    Tytuł:
    Weak uniform normal structure and iterative fixed points of nonexpansive mappings
    Autorzy:
    Domínguez Benavides, T.
    López Acedo, G.
    Xu, Hong
    Powiązania:
    https://bibliotekanauki.pl/articles/967052.pdf
    Data publikacji:
    1995
    Wydawca:
    Polska Akademia Nauk. Instytut Matematyczny PAN
    Tematy:
    nonexpansive mapping
    iterative fixed point
    geometrical coefficients of Banach spaces
    James' quasi-reflexive space
    weak uniform normal structure
    Opis:
    This paper is concerned with weak uniform normal structure and iterative fixed points of nonexpansive mappings. Precisely, in Section 1, we show that the geometrical coefficient β(X) for a Banach space X recently introduced by Jimenez-Melado [8] is exactly the weakly convergent sequence coefficient WCS(X) introduced by Bynum [1] in 1980. We then show in Section 2 that all kinds of James' quasi-reflexive spaces have weak uniform normal structure. Finally, in Section 3, we show that in a space X with weak uniform normal structure, every nonexpansive self-mapping defined on a weakly sequentially compact convex subset of X admits an iterative fixed point.
    Źródło:
    Colloquium Mathematicum; 1995, 68, 1; 17-23
    0010-1354
    Pojawia się w:
    Colloquium Mathematicum
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    Some fixed point theorems for G-nonexpansive mappings on ultrametric spaces and non-Archimedean normed spaces with a graph
    Autorzy:
    Mamghaderi, H.
    Masiha, H. P.
    Powiązania:
    https://bibliotekanauki.pl/articles/357892.pdf
    Data publikacji:
    2016
    Wydawca:
    Politechnika Rzeszowska im. Ignacego Łukasiewicza. Oficyna Wydawnicza
    Tematy:
    fixed point
    ultrametric space
    non-Archimedean space
    nonexpansive mapping
    connected graph
    punkt stały
    przestrzeń metryczna
    odwzorowanie nieekspansywne
    graf spójny
    Opis:
    A very interesting approach in the theory of fixed point is some general structures was recently given by Jachymski by using the context of metric spaces endowed with a graph. The purpose of this article is to present some new fixed point results for G-nonexpansive mappings defined on an ultrametric space and non-Archimedean normed space which are endowed with a graph. In particular, we investigate the relationship between weak connectivity graph and the existence of fixed point for these mappings.
    Źródło:
    Journal of Mathematics and Applications; 2016, 39; 81-90
    1733-6775
    2300-9926
    Pojawia się w:
    Journal of Mathematics and Applications
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    On the Existence of Common Fixed Points for Semigroups of Nonlinear Mappings in Modular Function Spaces
    Autorzy:
    Kozlowski, Wojciech M.
    Powiązania:
    https://bibliotekanauki.pl/articles/745208.pdf
    Data publikacji:
    2011
    Wydawca:
    Polskie Towarzystwo Matematyczne
    Tematy:
    Fixed point
    common fixed point
    nonexpansive mapping
    contractions
    semigroup of mappings
    modular function space
    modular space
    Orlicz space
    Musielak-Orlicz space
    Opis:
    Let \(C\) be a \(\rho\)-bounded, \(\rho\)-closed, convex subset of a modular function space \(L_\rho\). We investigate the existence of common fixed points for semigroups of nonlinear mappings \(T_t\colon C\to C\), i.e. a family such that \(T_0(x) = x\), \(T_{s+t} = T_s (T_t (x))\), where each \(T_t\) is either \(\rho\)-contraction or \(\rho\)-nonexpansive. We also briefly discuss existence of such semigroups and touch upon applications to differential equations.
    Źródło:
    Commentationes Mathematicae; 2011, 51, 1
    0373-8299
    Pojawia się w:
    Commentationes Mathematicae
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    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
    Tytuł:
    Ergodic properties of random infinite products of nonexpansive mappings
    Autorzy:
    Reich, S.
    Zaslavski, A. J.
    Powiązania:
    https://bibliotekanauki.pl/articles/357844.pdf
    Data publikacji:
    2017
    Wydawca:
    Politechnika Rzeszowska im. Ignacego Łukasiewicza. Oficyna Wydawnicza
    Tematy:
    complete metric space
    hyperbolic space
    infinite product
    nonexpansive mapping
    random weak ergodic property
    przestrzeń metryczna pełna
    przestrzeń hiperboliczna
    produkt nieskończony
    mapowanie
    własności ergodyczne
    Opis:
    In this paper we are concerned with the asymptotic behavior of random (unrestricted) infinite products of nonexpansive selfmappings of closed and convex subsets of a complete hyperbolic space. In contrast with our previous work in this direction, we no longer assume that these subsets are bounded. We first establish two theorems regarding the stability of the random weak ergodic property and then prove a related generic result. These results also extend our recent investigations regarding nonrandom infinite products.
    Źródło:
    Journal of Mathematics and Applications; 2017, 40; 149-159
    1733-6775
    2300-9926
    Pojawia się w:
    Journal of Mathematics and Applications
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    The generalized Day norm. Part II. Applications
    Autorzy:
    Budzyńska, Monika
    Grzesik, Aleksandra
    Kot, Mariola
    Powiązania:
    https://bibliotekanauki.pl/articles/747182.pdf
    Data publikacji:
    2017
    Wydawca:
    Uniwersytet Marii Curie-Skłodowskiej. Wydawnictwo Uniwersytetu Marii Curie-Skłodowskiej
    Tematy:
    Diametrically complete set
    Day norm, fixed point
    Kadec-Klee property
    LUR space
    nonexpansive mapping
    non-strict Opial property
    1-unconditional Schauder bases
    Opis:
    In this paper we prove that for each \(1< p, \tilde{p} < \infty\), the Banach space \((l^{\tilde{p}}, \left\|\cdot\right\|_{\tilde{p}})\) can be equivalently renormed in such a way that  the Banach space \((l^{\tilde{p}},\left\|\cdot\right\|_{L,\alpha,\beta,p,\tilde{p}})\) is LUR and has a diametrically complete set with empty interior. This result extends the Maluta theorem about existence of such a set in \(l^2\) with the Day norm. We also show that the Banach space \((l^{\tilde{p}},\left\|\cdot\right\|_{L,\alpha,\beta,p,\tilde{p}})\) has the weak fixed point property for nonexpansive mappings.
    Źródło:
    Annales Universitatis Mariae Curie-Skłodowska, sectio A – Mathematica; 2017, 71, 2
    0365-1029
    2083-7402
    Pojawia się w:
    Annales Universitatis Mariae Curie-Skłodowska, sectio A – Mathematica
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    On Nonlinear Differential Equations in Generalized Musielak-Orlicz Spaces
    Autorzy:
    Kozlowski, W.M.
    Powiązania:
    https://bibliotekanauki.pl/articles/744903.pdf
    Data publikacji:
    2013
    Wydawca:
    Polskie Towarzystwo Matematyczne
    Tematy:
    ordinary differential equation, nonlinear equation, Cauchy problem, initial value problem, fixed point, nonexpansive mapping, modular function space, Orlicz space, Musielak-Orlicz space, convex modular
    Opis:
    We consider ordinary differential equations \(u'(t)+(I-T)u(t)=0\), where an unknown function takes its values in a given modular function space being a generalization of Musielak-Orlicz spaces, and \(T\) is nonlinear mapping which is nonexpansive in the modular sense. We demonstrate that under certain natural assumptions the Cauchy problem related to this equation can be solved. We also show a process for the construction of such a solution. This result is then linked to the recent results of the fixed point theory in modular function spaces.
    Źródło:
    Commentationes Mathematicae; 2013, 53, 2
    0373-8299
    Pojawia się w:
    Commentationes Mathematicae
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    De la Vallée Poussin Summability, the Combinatorial Sum $\sum_{k=n}^{2n-1}$ (2k/k) and the de la Vallée Poussin Means Expansion
    Autorzy:
    Ali, Z. S.
    Powiązania:
    https://bibliotekanauki.pl/articles/357696.pdf
    Data publikacji:
    2017
    Wydawca:
    Politechnika Rzeszowska im. Ignacego Łukasiewicza. Oficyna Wydawnicza
    Tematy:
    complete metric space
    hyperbolic space
    infinite product
    nonexpansive mapping
    random weak ergodic property
    przestrzeń metryczna całkowita
    przestrzeń hiperboliczna
    produkt nieskończony
    mapowanie
    własności ergodyczne
    Opis:
    In this paper we apply the de la Vallee Poussin sum to a combinatorial Chebyshev sum by Ziad S. Ali in [1]. One outcome of this consideration is the main lemma proving the following combinatorial identity: with $Re(z)$ standing for the real part of z we have \[ \sum_{k=n}^{2n-1}\left({2k \atop k}\right) = Re\left(\left({2k \atop k}\right) \text{}_{2}F_{1}(1, 1/2 + n; 1 + n; 4\right) - \left({4n \atop 2n}\right) \text{}_{2}F_{1}(1, 1/2 + 2n; 1 + 2n; 4) \] Our main lemma will indicate in its proof that the hypergeometric factors \[ _{2}F_{1}(1, 1/2 + n; 1 + n; 4); \text{ and } _{2}F_{1}(1, 1/2 + 2n; 1 + 2n; 4) \] are complex, each having a real and imaginary part. As we apply the de la Vallee Poussin sum to the combinatorial Chebyshev sum generated in the Key lemma by Ziad S. Ali in [1], we see in the proof of the main lemma the extreme importance of the use of the main properties of the gamma function. This represents a second important consideration. A third new outcome are two interesting identities of the hypergeometric type with their new Meijer G function analogues. A fourth outcome is that by the use of the Cauchy integral formula for the derivatives we are able to give a dierent meaning to the sum: \[ \sum_{k=n}^{2n-1}\left({2k \atop k}\right) \] A fifth outcome is that by the use of the Gauss-Kummer formula we are able to make better sense of the expressions \[ \left({2n \atop n}\right)\text{}_{2}F_{1}(1, 1/2 + n; 1 + n; 4), \text{ and } \left({4n \atop 2n}\right)\text{}_{2}F_{1}(1, 1/2 + 2n; 1 + 2n; 4) \] by making use of the series denition of the hypergeometric function. As we continue we notice a new close relation of the Key lemma, and the de la Vallee Poussin means. With this close relation we were able to talk about P the de la Vallee Poussin summability of the two innite series $\sum_{n=0}^{\infty}\cos n\theta$ and $\sum_{n=0}^{\infty}(-1)^{n}\cos n\theta$. Furthermore the application of the de la Vallee Poussin sum to the Key lemma has created two new expansions representing the following functions: \[ \frac{2^{(n-1)}(1+x)^{n}(-1+2^{n}(1+x)^{n})}{n(2x+1)}, \text{ where } x=\cos \theta \] and \[ \frac {-2^{(n-1)}(-1 + 2^{n}(1-x)^{n})(1-x)^{n}} {n(2x - 1)}, \text{ where } x=\cos \theta \] in terms of the de la Vall´ee Poussin means of the two infinite series \[ \sum_{n=0}^{\infty}\cos\theta, \] and \[ \sum_{n=0}^{\infty}(-1)^{n}\cos\theta, \]
    Źródło:
    Journal of Mathematics and Applications; 2017, 40; 5-20
    1733-6775
    2300-9926
    Pojawia się w:
    Journal of Mathematics and Applications
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    On the construction of common fixed points for semigroups of nonlinear mappings in uniformly convex and uniformly smooth Banach spaces
    Autorzy:
    Kozlowski, W.M.
    Powiązania:
    https://bibliotekanauki.pl/articles/746293.pdf
    Data publikacji:
    2012
    Wydawca:
    Polskie Towarzystwo Matematyczne
    Tematy:
    common fixed point
    Fixed point
    Lipschitzian mapping
    pointwise Lipschitzian mapping
    semigroup of mappings
    asymptotic pointwise nonexpansive mapping
    uniformly convex Banach space
    uniformly smooth Banach space
    Fréchet differentiable norm
    weak compactness
    fixed point iteration process
    Krasnosel'skii-Mann process
    Mann process
    Ishikawa process
    Opis:
    Let \(C\) be a bounded, closed, convex subset of a uniformly convex and uniformly smooth Banach space \(X\). We investigate the weak convergence of the generalized Krasnosel'skii-Mann and Ishikawa iteration processes to common fixed points of semigroups of nonlinear mappings \(T_t\colon C \to C\). Each of \(T_t\) is assumed to be pointwise Lipschitzian, that is, there exists a family of functions \(\alpha_t\colon C \to [0, \infty)\) such that \(\|T_t(x) - T_t (y)\| \leq\alpha_t (x)\|x -y\|\) for \(x, y \in C\). The paper demonstrates how the weak compactness of \(C\) plays an essential role in proving the weak convergence of these processes to common fixed points.
    Źródło:
    Commentationes Mathematicae; 2012, 52, 2
    0373-8299
    Pojawia się w:
    Commentationes Mathematicae
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    An algorithm for finding a common solution for a system of mixed equilibrium problem, quasi-variational inclusion problem and fixed point problem of nonexpansive semigroup
    Autorzy:
    Min, L.
    Chang, S.
    Zuo, P.
    Powiązania:
    https://bibliotekanauki.pl/articles/255589.pdf
    Data publikacji:
    2010
    Wydawca:
    Akademia Górniczo-Hutnicza im. Stanisława Staszica w Krakowie. Wydawnictwo AGH
    Tematy:
    nonexpansive semigroup
    mixed equilibrium problem
    viscosity approximation method
    quasi-variational inclusion problem
    multi-valued maximal monotone mappings
    alpha-inverse-strongly monotone mapping
    Opis:
    In this paper, we introduce a hybrid iterative scheme for finding a common element of the set of solutions for a system of mixed equilibrium problems, the set of common fixed points for a nonexpansive semigroup and the set of solutions of the quasi-variational inclusion problem with multi-valued maximal monotone mappings and inverse-strongly monotone mappings in a Hilbert space. Under suitable conditions, some strong convergence theorems are proved. Our results extend some recent results in the literature.
    Źródło:
    Opuscula Mathematica; 2010, 30, 4; 465-484
    1232-9274
    2300-6919
    Pojawia się w:
    Opuscula Mathematica
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
      Wyświetlanie 1-14 z 14

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