The functional equation
James C. Lillo (1967)
Annales Polonici Mathematici
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James C. Lillo (1967)
Annales Polonici Mathematici
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Mathew O. Omeike (2015)
Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica
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In this paper we study the boundedness of solutions of some third-order delay differential equation in which is not necessarily differentiable but satisfy a Routh–Hurwitz condition in a closed interval .
Z. Krzeszowiak (1969)
Annales Polonici Mathematici
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Z. Kominek (1974)
Annales Polonici Mathematici
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C. T. Ng (1973)
Annales Polonici Mathematici
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H. Światak (1967)
Annales Polonici Mathematici
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M. Malenica (1982)
Matematički Vesnik
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Teresa Janiak, Elżbieta Łuczak-Kumorek (1996)
Discussiones Mathematicae, Differential Inclusions, Control and Optimization
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The basic idea of this paper is to give the existence theorem and the method of averaging for the system of functional-differential inclusions of the form ⎧ (0) ⎨ ⎩ (1)
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.
H. Swiatak (1968)
Matematički Vesnik
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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.
Maciej Sablik (1998)
Annales Polonici Mathematici
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We deal with the linear functional equation (E) , where g:(0,∞) → (0,∞) is unknown, is a probability distribution, and ’s are positive numbers. The equation (or some equivalent forms) was considered earlier under different assumptions (cf. [1], [2], [4], [5] and [6]). Using Bernoulli’s Law of Large Numbers we prove that g has to be constant provided it has a limit at one end of the domain and is bounded at the other end.
Joachim Cuntz, Siegfried Echterhoff, Xin Li (2015)
Journal of the European Mathematical Society
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We compute the -theory of -algebras generated by the left regular representation of left Ore semigroups satisfying certain regularity conditions. Our result describes the -theory of these semigroup -algebras in terms of the -theory for the reduced group -algebras of certain groups which are typically easier to handle. Then we apply our result to specific semigroups from algebraic number theory.
Yasutaka Sibuya (1984)
Recherche Coopérative sur Programme n°25
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D. Przeworska-Rolewicz, S. Rolewicz (1967)
Annales Polonici Mathematici
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S. Blunck, L. Weis (2001)
Studia Mathematica
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Let be a C₀ semigroup with generator A on a Banach space X and let be an operator ideal, e.g. the class of compact, Hilbert-Schmidt or trace class operators. We show that the resolvent R(λ,A) of A belongs to if and only if the integrated semigroup belongs to . For analytic semigroups, implies , and in this case we give precise estimates for the growth of the -norm of (e.g. the trace of ) in terms of the resolvent growth and the imbedding D(A) ↪ X.
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...
Jan Okniński (2002)
Colloquium Mathematicae
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The semigroup of subspaces of the algebra of 2 × 2 matrices over a finite field is studied. The ideal structure of S, the regular -classes of S and the structure of the complex semigroup algebra ℂ[S] are described.
Dorota Krassowska, Janusz Matkowski (2005)
Annales Polonici Mathematici
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It is shown that, under some general algebraic conditions on fixed real numbers a,b,α,β, every solution f:ℝ → ℝ of the system of functional inequalities f(x+a) ≤ f(x)+α, f(x+b) ≤ f(x)+β that is continuous at some point must be a linear function (up to an additive constant). Analogous results for three other similar simultaneous systems are presented. An application to a characterization of -norm is given.
Giovanni Dore, Alberto Venni (2005)
Studia Mathematica
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We give a concise exposition of the basic theory of functional calculus for N-tuples of sectorial or bisectorial operators, with respect to operator-valued functions; moreover we restate and prove in our setting a result of N. Kalton and L. Weis about the boundedness of the operator when f is an R-bounded operator-valued holomorphic function.
Jolanta Olko (2005)
Annales Polonici Mathematici
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Let be an iteration semigroup of linear continuous set-valued functions. If the semigroup has an infinitesimal operator then it is a uniformly continuous semigroup majorized by an exponential semigroup. Moreover, for sufficiently small t every linear selection of is invertible and there exists an exponential semigroup of linear continuous selections of .
Bing Gen Zhang, Shu Tang Liu (1995)
Discussiones Mathematicae, Differential Inclusions, Control and Optimization
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This paper is concerned with the delay partial difference equation (1) where are real numbers, and are nonnegative integers, u is a positive integer. Sufficient and necessary conditions for all solutions of (1) to be oscillatory are obtained.