Continuous solutions of the functional equation for vector-valued functions φ
Z. Krzeszowiak (1969)
Annales Polonici Mathematici
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Z. Krzeszowiak (1969)
Annales Polonici Mathematici
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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)
James C. Lillo (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.
Lech Drewnowski (2020)
Commentationes Mathematicae Universitatis Carolinae
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We discuss various results on the existence of ‘true’ preimages under continuous open maps between -spaces, -lattices and some other spaces. The aim of the paper is to provide accessible proofs of this sort of results for functional-analysts.
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.
Tomáš G. Roskovec, Filip Soudský (2023)
Kybernetika
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The weak lower semicontinuity of the functional is a classical topic that was studied thoroughly. It was shown that if the function is continuous and convex in the last variable, the functional is sequentially weakly lower semicontinuous on . However, the known proofs use advanced instruments of real and functional analysis. Our aim here is to present a proof understandable even for students familiar only with the elementary measure theory.
H. Swiatak (1968)
Matematički Vesnik
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H. G. Dales, M. Daws, H. L. Pham, P. Ramsden
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The theory of multi-norms was developed by H. G. Dales and M. E. Polyakov in a memoir that was published in Dissertationes Mathematicae. In that memoir, the notion of ’equivalence’ of multi-norms was defined. In the present memoir, we make a systematic study of when various pairs of multi-norms are mutually equivalent. In particular, we study when (p,q)-multi-norms defined on spaces are equivalent, resolving most cases; we have stronger results in the case where r = 2. We also show...
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.
Z. Kominek (1974)
Annales Polonici Mathematici
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C. T. Ng (1973)
Annales Polonici Mathematici
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M. Malenica (1982)
Matematički Vesnik
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H. Światak (1967)
Annales Polonici Mathematici
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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.
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.
Mohammed Hemdaoui (2019)
Mathematica Bohemica
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We show that some unital complex commutative LF-algebra of -tempered functions on (M. Hemdaoui, 2017) equipped with its natural convex vector bornology is useful for functional calculus.
J. Eweret (1989)
Matematički Vesnik
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Malgorzata Wójcicka (1986)
Colloquium Mathematicae
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Hôǹg Thái Nguyêñ, Maciej Juniewicz, Jolanta Ziemińska (2001)
Studia Mathematica
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We present a new continuous selection theorem, which unifies in some sense two well known selection theorems; namely we prove that if F is an H-upper semicontinuous multivalued map on a separable metric space X, G is a lower semicontinuous multivalued map on X, both F and G take nonconvex -decomposable closed values, the measure space T with a σ-finite measure μ is nonatomic, 1 ≤ p < ∞, is the Bochner-Lebesgue space of functions defined on T with values in a Banach space E, F(x)...