-solutions of a system of functional equations
Z. Kominek (1974)
Annales Polonici Mathematici
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Z. Kominek (1974)
Annales Polonici Mathematici
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Janusz Morawiec, Ludwig Reich (2005)
Bulletin of the Polish Academy of Sciences. Mathematics
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Let 0 < β < α < 1 and let p ∈ (0,1). We consider the functional equation φ(x) = pφ (x-β)/(1-β) + (1-p)φ(minx/α, (x(α-β)+β(1-α))/α(1-β)) and its solutions in two classes of functions, namely ℐ = φ: ℝ → ℝ|φ is increasing, , , = φ: ℝ → ℝ|φ is continuous, , . We prove that the above equation has at most one solution in and that for some parameters α,β and p such a solution exists, and for some it does not. We also determine all solutions of the equation in ℐ and we show the...
C. T. Ng (1973)
Annales Polonici Mathematici
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H. Światak (1967)
Annales Polonici Mathematici
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László Simon (2015)
Mathematica Bohemica
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We consider second order quasilinear evolution equations where also the main part contains functional dependence on the unknown function. First, existence of solutions in is proved and examples satisfying the assumptions of the existence theorem are formulated. Then a uniqueness theorem is proved. Finally, existence and some qualitative properties of the solutions in (boundedness and stabilization as ) are shown.
M. Malenica (1982)
Matematički Vesnik
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Feng Qin (2015)
Kybernetika
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Commuting is an important property in any two-step information merging procedure where the results should not depend on the order in which the single steps are performed. In the case of bisymmetric aggregation operators with the neutral elements, Saminger, Mesiar and Dubois, already reduced characterization of commuting -ary operators to resolving the unary distributive functional equations. And then the full characterizations of these equations are obtained under the assumption that...
Yasutaka Sibuya (1984)
Recherche Coopérative sur Programme n°25
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Adam Bobrowski, Radosław Bogucki (2008)
Studia Mathematica
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Let be a locally compact Hausdorff space. Let , i = 0,1,...,N, be generators of Feller semigroups in C₀() with related Feller processes and let , i = 0,...,N, be non-negative continuous functions on with . Assume that the closure A of defined on generates a Feller semigroup T(t), t ≥ 0 in C₀(). A natural interpretation of a related Feller process X = X(t), t ≥ 0 is that it evolves according to the following heuristic rules: conditional on being at a point p ∈ , with probability...
(2013)
Colloquium Mathematicae
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We consider one-parameter (C₀)-semigroups of operators in the space with infinitesimal generator of the form where G is an -valued rapidly decreasing distribution on ℝⁿ. It is proved that the Petrovskiĭ condition for forward evolution ensures not only the existence and uniqueness of the above semigroup but also its nice behaviour after restriction to whichever of the function spaces , , p ∈ [1,∞], , a ∈ ]0,∞[, or the spaces , q ∈ ]1,∞], of bounded distributions.
Min Zhang, Jianguo Si (2014)
Annales Polonici Mathematici
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This work deals with Feigenbaum’s functional equation ⎧ , ⎨ ⎩ g(0) = 1, -1 ≤ g(x) ≤ 1, x∈[-1,1] where p ≥ 2 is an integer, is the p-fold iteration of g, and h is a strictly monotone odd continuous function on [-1,1] with h(0) = 0 and |h(x)| < |x| (x ∈ [-1,1], x ≠ 0). Using a constructive method, we discuss the existence of continuous unimodal even solutions of the above equation.
Thomas Kalmes (2010)
Studia Mathematica
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We show that if Ω is an open subset of ℝ², then the surjectivity of a partial differential operator P(D) on the space of ultradistributions of Beurling type is equivalent to the surjectivity of P(D) on .
Alejandro Ramírez, Vladas Sidoravicius (2004)
Journal of the European Mathematical Society
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We study a continuous time growth process on the -dimensional hypercubic lattice , which admits a phenomenological interpretation as the combustion reaction , where represents heat particles and inert particles. This process can be described as an interacting particle system in the following way: at time 0 a simple symmetric continuous time random walk of total jump rate one begins to move from the origin of the hypercubic lattice; then, as soon as any random walk visits a site...
Cédric Arhancet (2013)
Studia Mathematica
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We give sufficient conditions on an operator space E and on a semigroup of operators on a von Neumann algebra M to obtain a bounded analytic or R-analytic semigroup ( on the vector valued noncommutative -space . Moreover, we give applications to the functional calculus of the generators of these semigroups, generalizing some earlier work of M. Junge, C. Le Merdy and Q. Xu.
Vladislav Vysotsky (2014)
Annales de l'I.H.P. Probabilités et statistiques
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Take a centered random walk and consider the sequence of its partial sums . Suppose is in the domain of normal attraction of an -stable law with . Assuming that is either right-exponential (i.e. for some and all ) or right-continuous (skip free), we prove that as , where depends on the distribution of the walk. We also consider a conditional version of this problem and study positivity of integrated discrete bridges.
Malkhaz Ashordia (2016)
Mathematica Bohemica
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The Cauchy problem for the system of linear generalized ordinary differential equations in the J. Kurzweil sense , with a unique solution is considered. Necessary and sufficient conditions are obtained for a sequence of the Cauchy problems , to have a unique solution for any sufficiently large such that uniformly on . Presented results are analogous to the sufficient conditions due to Z. Opial for linear ordinary differential systems....