On the functional equation
H. Swiatak (1968)
Matematički Vesnik
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H. Swiatak (1968)
Matematički Vesnik
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Valeriĭ A. Faĭziev, Prasanna K. Sahoo (2013)
Mathematica Bohemica
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Let be a group and an abelian group. Let be the set of solutions of the Jensen functional equation satisfying the condition for all . Let be the set of solutions of the quadratic equation satisfying the Kannappan condition for all . In this paper we determine solutions of the Whitehead equation on groups. We show that every solution of the Whitehead equation is of the form , where and . Moreover, if has the additional property that implies for all ,...
Fouad Lehlou, Mohammed Moussa, Ahmed Roukbi, Samir Kabbaj (2016)
Annales Universitatis Paedagogicae Cracoviensis. Studia Mathematica
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In this paper, we study the superstablity problem of the cosine and sine type functional equations: f(xσ(y)a)+f(xya)=2f(x)f(y) and f(xσ(y)a)−f(xya)=2f(x)f(y), where f : S → ℂ is a complex valued function; S is a semigroup; σ is an involution of S and a is a fixed element in the center of S.
James C. Lillo (1967)
Annales Polonici Mathematici
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Z. Krzeszowiak (1969)
Annales Polonici Mathematici
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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.
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)
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.
Iz-iddine EL-Fassi (2016)
Annales Universitatis Paedagogicae Cracoviensis. Studia Mathematica
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The aim of this paper is to study the superstability problem of the d’Alembert type functional equation f(x+y+z)+f(x+y+σ(z))+f(x+σ(y)+z)+f(σ(x)+y+z)=4f(x)f(y)f(z) for all x, y, z ∈ G, where G is an abelian group and σ : G → G is an endomorphism such that σ(σ(x)) = x for an unknown function f from G into ℂ or into a commutative semisimple Banach algebra.
C. T. Ng (1973)
Annales Polonici Mathematici
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Z. Kominek (1974)
Annales Polonici Mathematici
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Rosanna Villella-Bressan (1985)
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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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.
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.