Multivalued pseudo-contractive mappings defined on unbounded sets in Banach spaces

Claudio H. Morales

Displaying similar documents to “Multivalued pseudo-contractive mappings defined on unbounded sets in Banach spaces”

Fredholmness of pseudo-differential operators with nonregular symbols

Kazushi Yoshitomi (2023)

Czechoslovak Mathematical Journal

Similarity:

We establish the Fredholmness of a pseudo-differential operator whose symbol is of class $C^{0, σ}$ , $0 < σ < 1$ , in the spatial variable. Our work here refines the work of H. Abels, C. Pfeuffer (2020).

Continuous pseudo-hairy spaces and continuous pseudo-fans

Janusz R. Prajs (2002)

Fundamenta Mathematicae

Similarity:

A compact metric space X̃ is said to be a continuous pseudo-hairy space over a compact space X ⊂ X̃ provided there exists an open, monotone retraction $r : X ̃ \binom{o n t o}{⟶} X$ such that all fibers $r^{- 1} (x)$ are pseudo-arcs and any continuum in X̃ joining two different fibers of r intersects X. A continuum $Y_{X}$ is called a continuous pseudo-fan of a compactum X if there are a point $c \in Y_{X}$ and a family ℱ of pseudo-arcs such that $⋃ ℱ = Y_{X}$ , any subcontinuum of $Y_{X}$ intersecting two different elements of ℱ contains c, and ℱ is homeomorphic...

The Brouwer Fixed Point Theorem for Some Set Mappings

Dariusz Miklaszewski (2013)

Bulletin of the Polish Academy of Sciences. Mathematics

Similarity:

For some classes $X \subset 2^{ₙ}$ of closed subsets of the disc ₙ ⊂ ℝⁿ we prove that every Hausdorff-continuous mapping f: X → X has a fixed point A ∈ X in the sense that the intersection A ∩ f(A) is nonempty.

Pseudo-boundaries and pseudo-interiors for topological convexities

M. Van de Vel

Similarity:

CONTENTS0. Introduction......... .............................................................51. Topological convexity structures.......................................62. Half-spaces and related results......................................123. Pseudo-boundaries........................................................254. The Krein-Milman theorem.............................................335. Pseudo-interiority...........................................................406. The existence...

Ruelle operator with nonexpansive IFS

Ka-Sing Lau, Yuan-Ling Ye (2001)

Studia Mathematica

Similarity:

The Ruelle operator and the associated Perron-Frobenius property have been extensively studied in dynamical systems. Recently the theory has been adapted to iterated function systems (IFS) $(X, {w_{j}}_{j = 1}^{m}, {p_{j}}_{j = 1}^{m})$ , where the $w_{j}$ ’s are contractive self-maps on a compact subset $X \subseteq ℝ^{d}$ and the $p_{j}$ ’s are positive Dini functions on X [FL]. In this paper we consider Ruelle operators defined by weakly contractive IFS and nonexpansive IFS. It is known that in such cases, positive bounded eigenfunctions may not exist in general....

On sets of confluent and related mappings in the space $Y^{X}$

T. Maćkowiak (1976)

Colloquium Mathematicae

Similarity:

Generalized notions of amenability for a class of matrix algebras

Amir Sahami (2019)

Commentationes Mathematicae Universitatis Carolinae

Similarity:

We investigate the amenability and its related homological notions for a class of $I \times I$ -upper triangular matrix algebra, say $UP (I, A)$ , where $A$ is a Banach algebra equipped with a nonzero character. We show that $UP (I, A)$ is pseudo-contractible (amenable) if and only if $I$ is singleton and $A$ is pseudo-contractible (amenable), respectively. We also study pseudo-amenability and approximate biprojectivity of $UP (I, A)$ .

Fixed points of periodic and firmly lipschitzian mappings in Banach spaces

Krzysztof Pupka (2012)

Commentationes Mathematicae Universitatis Carolinae

Similarity:

W.A. Kirk in 1971 showed that if $T : C \to C$ , where $C$ is a closed and convex subset of a Banach space, is $n$ -periodic and uniformly $k$ -lipschitzian mapping with $k < k_{0} (n)$ , then $T$ has a fixed point. This result implies estimates of $k_{0} (n)$ for natural $n \geq 2$ for the general class of $k$ -lipschitzian mappings. In these cases, $k_{0} (n)$ are less than or equal to 2. Using very simple method we extend this and later results for a certain subclass of the family of $k$ -lipschitzian mappings. In the paper we show that $k_{0} (3) > 2$ in any Banach...

On a question of Demailly-Peternell-Schneider

Meng Chen, Qi Zhang (2013)

Journal of the European Mathematical Society

Similarity:

We give an affirmative answer to an open question posed by Demailly-Peternell-Schneider in 2001 and recently by Peternell. Let $f : X \to Y$ be a surjective morphism from a log canonical pair $(X, D)$ onto a $ℚ$ -Gorenstein variety $Y$ . If $- (K_{X} + D)$ is nef, we show that $- K_{Y}$ is pseudo-effective.

The generalized Day norm. Part II. Applications

Monika Budzyńska, Aleksandra Grzesik, Mariola Kot (2017)

Annales Universitatis Mariae Curie-Sklodowska, sectio A – Mathematica

Similarity:

In this paper we prove that for each $1 < p, \tilde{p} < \infty$ , the Banach space $(l^{\tilde{p}}, {∥\cdot∥}_{\tilde{p}})$ can be equivalently renormed in such a way that the Banach space $(l^{\tilde{p}}, {∥\cdot∥}_{L, α, β, p, \tilde{p}})$ 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 $(l^{\tilde{p}}, {∥\cdot∥}_{L, α, β, p, \tilde{p}})$ has the weak fixed point property for nonexpansive mappings.

Fixed point approximation under Mann iteration beyond Ishikawa

Anthony Hester, Claudio H. Morales (2020)

Commentationes Mathematicae Universitatis Carolinae

Similarity:

Consider the Mann iteration $x_{n + 1} = (1 - α_{n}) x_{n} + α_{n} T x_{n}$ for a nonexpansive mapping $T : K \to K$ defined on some subset $K$ of the normed space $X$ . We present an innovative proof of the Ishikawa almost fixed point principle for nonexpansive mapping that reveals deeper aspects of the behavior of the process. This fact allows us, among other results, to derive convergence of the process under the assumption of existence of an accumulation point of ${x_{n}}$ .

Reflexivity and approximate fixed points

Eva Matoušková, Simeon Reich (2003)

Studia Mathematica

Similarity:

A Banach space X is reflexive if and only if every bounded sequence xₙ in X contains a norm attaining subsequence. This means that it contains a subsequence $x_{n_{k}}$ for which $s u p_{f \in S_{X *}} l i m s u p_{k \to \infty} f (x_{n_{k}})$ is attained at some f in the dual unit sphere $S_{X *}$ . A Banach space X is not reflexive if and only if it contains a normalized sequence xₙ with the property that for every $f \in S_{X *}$ , there exists $g \in S_{X *}$ such that $l i m s u p_{n \to \infty} f (x ₙ) < l i m i n f_{n \to \infty} g (x ₙ)$ . Combining this with a result of Shafrir, we conclude that every infinite-dimensional Banach space contains an unbounded...

Birational Finite Extensions of Mappings from a Smooth Variety

Marek Karaś (2009)

Bulletin of the Polish Academy of Sciences. Mathematics

Similarity:

We present an example of finite mappings of algebraic varieties f:V → W, where V ⊂ kⁿ, $W \subset k^{n + 1}$ , and $F : k ⁿ \to k^{n + 1}$ such that ${F |}_{V} = f$ and gdeg F = 1 < gdeg f (gdeg h means the number of points in the generic fiber of h). Thus, in some sense, the result of this note improves our result in J. Pure Appl. Algebra 148 (2000) where it was shown that this phenomenon can occur when V ⊂ kⁿ, $W \subset k^{m}$ with m ≥ n+2. In the case V,W ⊂ kⁿ a similar example does not exist.

Intrinsic pseudo-volume forms for logarithmic pairs

Thomas Dedieu (2010)

Bulletin de la Société Mathématique de France

Similarity:

We study an adaptation to the logarithmic case of the Kobayashi-Eisenman pseudo-volume form, or rather an adaptation of its variant defined by Claire Voisin, for which she replaces holomorphic maps by holomorphic $K$ -correspondences. We define an intrinsic logarithmic pseudo-volume form $Φ_{X, D}$ for every pair $(X, D)$ consisting of a complex manifold $X$ and a normal crossing Weil divisor $D$ on $X$ , the positive part of which is reduced. We then prove that $Φ_{X, D}$ is generically non-degenerate when $X$ is projective...