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1
Content available remote Stability of an AQCQ functional equation in non-Archimedean (n, β)-normed spaces
Liu Yachai, Yang Xiuzhong, Liu Guofen
Demonstratio Mathematica
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2019
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Vol. 52, nr 1
130--146
EN
In this paper, we adopt direct method to prove the Hyers-Ulam-Rassias stability of an additive-quadratic-cubic-quartic functional equation f(x+2y)+f(x-2y) = 4f(x+y)+4f(x-y)-6f(x)+f(2y)+f(-2y)-4f(y)-4f(-y) in non-Archimedean (n,β)-normed spaces.
2
Content available Solutions of some functional equations in a class of generalized Hölder functions
Lupa M.
Journal of Applied Mathematics and Computational Mechanics
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2016
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Vol. 15, nr 4
105--116
EN
The existence and uniqueness of solutions a nonlinear iterative equation in the class of r-times differentiable functions with the r-derivative satisfying a generalized Hölder condition is considered.
3
Content available On some characterization of an inverse proportionality type function
Domańska K.
Scientific Issues of Jan Długosz University in Częstochowa. Mathematics
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2014
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Vol. 19
175--178
EN
We deal with a functional equation of the form ƒ(x + y) = F(ƒ(x), ƒ(y)) (so called addition formula) assuming that the given binary operation F is associative but its domain is not connected. The aim of the present paper is to discuss solutions of the equation [formula]. It turns out that this functional equation characterized an inverse proportionality type function, but if the domain of the unknown function has no neutral element. In this paper we admit fairly general structure in the domain of the unknown function.
4
Content available The stability of the Dhombres-type trigonometric functional equation
Tyrala I.
Scientific Issues of Jan Długosz University in Częstochowa. Mathematics
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2012
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Vol. 17
87-96
EN
In the present paper we deal with the Dhombres-type trigonometric difference f(x + y 2 )2 – f(x − y 2)2 + f(x + y) + f(x − y) − f(x) [f(y) + g(y)], assuming that its absolute value is majorized by some constant. Our aim is to find functions and which satisfy the Dhombres-type trigonometric functional equation and for which the differences f - f and g - g are uniformly bounded.
5
Content available On some addition formulas for homographic type functions
Domańska K.
Scientific Issues of Jan Długosz University in Częstochowa. Mathematics
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2012
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Vol. 17
17-24
EN
We deal with the functional equation (so called addition formula) of the form f(x + y) = F(f(x),f(y)), where F is an associative rational function. The class of associative rational functions was described by A. Chéritat [1] and his work was followed by a paper of the author. For function F defined by F(x,y) = ϕ−1(ϕ(x) + ϕ(y)), where ϕ is a homographic function, the addition formula is fulfilled by homographic type functions. We consider the class of the associative rational functions defined by formula F(u,v) =uv αuv + u + v, where α is a fixed real numer.
6
Content available Solutions of the dhombres-type trigonometric functional equation
Tyrala I.
Scientific Issues of Jan Długosz University in Częstochowa. Mathematics
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2011
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Vol. 16
87--94
EN
Let (G, +) be a uniquely 2-divisible Abelian group. In the present paper we will consider the solutions of functional equation [f(x + y)]2 - [f(x - y)]2 + f(2x + 2y) + f(2x - 2y) = f(2x)[f(2y) + 2g(2y)], x,y ϵ G, where f and g are complex-valued functions defined on G.
7
Content available A characterization of a homographic type function II
Domańska K.
Scientific Issues of Jan Długosz University in Częstochowa. Mathematics
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2011
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Vol. 16
15--18
EN
This article is a continuation of the investigations contained in the previous paper [2]. We deal with the following conditional functional equation: [wzór] implies [wzór] with λ ≠ 0.
8
Content available On some generalizations of Gołąb-Schinzel functional equation
Matkowski J., Okrzesik J.
Scientific Issues of Jan Długosz University in Częstochowa. Mathematics
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2010
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Vol. 15
81--90
EN
Composite functional equations in several variables generalizing the Gołąb-Schinzel equation are considerd and some simple methods allowing us to determine their one-to-one solutions, bijective solutions or the solutions having exactly one zero are presented. For an arbitrarily fixed real p, the functional equation Φ([pφ(y) + (1−p)]x +[(1−p)φ(x)+p]y) = φ(x)φ(y), x,y ∈ R, being a special generalization of the Gołąb-Schinzel equation, is considered.
9
Content available A characterization of a homographic type function
Domańska K.
Scientific Issues of Jan Długosz University in Częstochowa. Mathematics
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2010
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Vol. 15
25--30
EN
We deal with a functional equation of the form f(x + y) = F(f(x),f(y)) (the so called addition formula) assuming that the given binary operation F is associative but its domain of definition is not necessarily connected. In the present paper we shall restrict our consideration to the case when [formula]. These considerations may be viewed as counter parts of Losonczi's [7] and Domańska's [3] results on local solutions of the functional equation f(F(x, y)) = f(x) + f(y) with the same behaviour of the given associative operation F. In this paper we admit fairly general structure in the domain of the unknown function.
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