Another fixed point theorem for nonexpansive potential operators

Biagio Ricceri

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Displaying similar documents to “Another fixed point theorem for nonexpansive potential operators”

Ruelle operator with nonexpansive IFS

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

Studia Mathematica

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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....

The generalized Day norm. Part II. Applications

Monika Budzyńska, Aleksandra Grzesik, Mariola Kot (2017)

Annales Universitatis Mariae Curie-Sklodowska, sectio A – Mathematica

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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.

Convergence of approximating fixed points sets for multivalued nonexpansive mappings

Paolamaria Pietramala (1991)

Commentationes Mathematicae Universitatis Carolinae

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Let $K$ be a closed convex subset of a Hilbert space $H$ and $T : K ⊸ K$ a nonexpansive multivalued map with a unique fixed point $z$ such that ${z} = T (z)$ . It is shown that we can construct a sequence of approximating fixed points sets converging in the sense of Mosco to $z$ .

On the separation properties of $K_{ω}$

Malgorzata Wójcicka (1986)

Colloquium Mathematicae

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

T. Maćkowiak (1976)

Colloquium Mathematicae

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Measures of noncompactness in locally convex spaces and fixed point theory for the sum of two operators on unbounded convex sets

Józef Banaś, Afif Ben Amar (2013)

Commentationes Mathematicae Universitatis Carolinae

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In this paper we prove a collection of new fixed point theorems for operators of the form $T + S$ on an unbounded closed convex subset of a Hausdorff topological vector space $(E, Γ)$ . We also introduce the concept of demi- $τ$ -compact operator and $τ$ -semi-closed operator at the origin. Moreover, a series of new fixed point theorems of Krasnosel’skii type is proved for the sum $T + S$ of two operators, where $T$ is $τ$ -sequentially continuous and $τ$ -compact while $S$ is $τ$ -sequentially continuous (and $Φ_{τ}$ -condensing,...

Reflexivity and approximate fixed points

Eva Matoušková, Simeon Reich (2003)

Studia Mathematica

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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...

On d-characteristic and $d_{Ξ}$ -characteristic of linear operators

D. Przeworska-Rolewicz, S. Rolewicz (1967)

Annales Polonici Mathematici

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$C^{r}$ -solutions of a system of functional equations

Z. Kominek (1974)

Annales Polonici Mathematici

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Generalized Hilbert Operators on Bergman and Dirichlet Spaces of Analytic Functions

Sunanda Naik, Karabi Rajbangshi (2015)

Bulletin of the Polish Academy of Sciences. Mathematics

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Let f be an analytic function on the unit disk . We define a generalized Hilbert-type operator $_{a, b}$ by $_{a, b} (f) (z) = Γ (a + 1) / Γ (b + 1) \int_{0}^{1} (f (t) {(1 - t)}^{b}) / ({(1 - t z)}^{a + 1}) d t$ , where a and b are non-negative real numbers. In particular, for a = b = β, $_{a, b}$ becomes the generalized Hilbert operator $_{β}$ , and β = 0 gives the classical Hilbert operator . In this article, we find conditions on a and b such that $_{a, b}$ is bounded on Dirichlet-type spaces $S^{p}$ , 0 < p < 2, and on Bergman spaces $A^{p}$ , 2 < p < ∞. Also we find an upper bound for the norm of the operator $_{a, b}$ ....

On the functional equation $f (x) + \sum_{i = 1}^{n} g_{i} (y_{i}) = h (T (x, y_{1}, y_{2}, . . ., y_{n}))$

C. T. Ng (1973)

Annales Polonici Mathematici

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Fixed point theorems for nonexpansive operators with dissipative perturbations in cones

Shih-sen Chang, Yu-Qing Chen, Yeol Je Cho, Byung-Soo Lee (1998)

Commentationes Mathematicae Universitatis Carolinae

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Let $P$ be a cone in a Hilbert space $H$ , $A : P \to 2^{P}$ be an accretive mapping (equivalently, $- A$ be a dissipative mapping) and $T : P \to P$ be a nonexpansive mapping. In this paper, some fixed point theorems for mappings of the type $- A + T$ are established. As an application, we utilize the results presented in this paper to study the existence problem of solutions for some kind of nonlinear integral equations in $L^{2} (Ω)$ .

On some symmetrical equations of the form $f_{1} (x_{1} + . . . + x_{n}) = \sum_{i_{1}, . . ., i_{n}}) f_{1} (x_{i} 1) . . . f_{n} (x_{i} n)$

H. Światak (1967)

Annales Polonici Mathematici

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