On the functional equation
H. Swiatak (1968)
Matematički Vesnik
Similarity:
H. Swiatak (1968)
Matematički Vesnik
Similarity:
Valeriĭ A. Faĭziev, Prasanna K. Sahoo (2013)
Mathematica Bohemica
Similarity:
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
Similarity:
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
Similarity:
Z. Krzeszowiak (1969)
Annales Polonici Mathematici
Similarity:
Dorota Krassowska, Janusz Matkowski (2005)
Annales Polonici Mathematici
Similarity:
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
Similarity:
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
Similarity:
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
Similarity:
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
Similarity:
Z. Kominek (1974)
Annales Polonici Mathematici
Similarity:
Rosanna Villella-Bressan (1985)
Annales Polonici Mathematici
Similarity:
M. Malenica (1982)
Matematički Vesnik
Similarity:
H. Światak (1967)
Annales Polonici Mathematici
Similarity:
Min Zhang, Jianguo Si (2014)
Annales Polonici Mathematici
Similarity:
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.
László Simon (2015)
Mathematica Bohemica
Similarity:
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.