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1
Content available remote The new investigation of the stability ofmixed type additive-quartic functionalequations in non-Archimedean spaces
Thanyacharoen Anurak, Sintunavarat Wutiphol
Demonstratio Mathematica
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2020
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Vol. 53, nr 1
174--192
EN
In this article, we prove the generalized Hyers-Ulam stability for the following additive-quarticfunctional equation: f(x + 3y) + f(x - 3y) + f(x + 2y) + f(x - 2y) + 22f(x) + 24f(y) = 13[ f(x + y) + f(x - y)] + 12f(2y), where f maps from an additive group to a complete non-Archimedean normed space.
2
Content available remote Solutions of some functional equations related to the determinant of certain matrices
Akkouchi M., Rhali M.
Demonstratio Mathematica
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2010
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Vol. 43, nr 1
97-106
EN
We solve the functional equation : [....] where K is a field which is not of characteristic 2 and f, g, h : K4 ->o K are unknown functions. We study also a class of functional equations of 2n variables generalizing the two equations above. This work is motivated by a paper of J. K. Chung and P. K. Sahoo published in 2002 and a recent paper of the authors published in 2005.
3
Content available remote On a sum form functional equation related to entropies and some moments of a discrete random variable
Nath P., Singh D.
Demonstratio Mathematica
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2009
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Vol. 42, nr 1
83-96
EN
The general solutions of a sum form functional equation have been obtained. The importance of its solutions in relation to the entropies and some moments of a discrete random variable has been discussed.
4
Content available remote Some inequalities connected with a quadratic functional equation
Troczka-Pawelec K.
Scientific Issues of Jan Długosz University in Częstochowa. Mathematics
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2008
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Vol. 13
73-79
EN
Let (X, +) be an Abelian group. One can show that a mapping f: X R satisfying the inequality f(x + y) + f(x-y)≤2f(x)+2f(y) (1) for all x, y ∈ X also satisfies the inequalities f(2x + y)≤4f(:c) + f (y) + f (x + y) - f (x - y) and f(2x+y) + f(2x -y)≤ 8f(x) + 2f(y) for all x, y ∈ X. A question of finding sufficient conditions under which the inequalities (1), (2) and (3) are equivalent will be considered. In this note, some properties of the solution of (1) will be proved. We also consider another definition of a subquadratic function given in [1].
5
Content available remote An invariance of the geometric mean with respect to Lagrangian conditionally homogeneous mean-type mappings
Głazowska D.
Demonstratio Mathematica
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2007
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Vol. 40, nr 2
289-302
EN
We determine all the Lagrangian conditionally homogeneous mean-type mappings for which the geometric mean is invariant.
6
Content available remote Stability of the Euler-Lagrange-Rassias functional equation
Pietrzyk A.
Demonstratio Mathematica
|
2006
|
Vol. 39, nr 3
523-530
EN
Let F be a field, a1, a2 is an element of F, K is an element of {R, C}, s an element of K\{0,1}, X be a linear space over F, S C is contained in X be nonempty, and Y be a Banach space over K. Under some additional assumptions on S we show some stability results for the functional equation Q (a1x + a2y) + Q (a2X - a1y) = s[Q{x) + Q{y)} in the class of function Q : S -> Y.
7
Content available remote Some remarks on subquadratic functions
Kominek Z., Troczka K.
Demonstratio Mathematica
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2006
|
Vol. 39, nr 4
751-758
EN
Some basic properties of subquadratic functions, i.e. functions fulfilling the inequality phi (x + y) + phi(x - y) is less than or equal to 2 phi(x) + 2 phi(y) are proved. In this note X be always a real linear space and R be denotes the set of all reals. Every function phi : X approaches R satisfying the following inequality (1) phi(x + y) + phi(x - y) is less than or equal 2phi(x) + 2phi(y), x, y is an element of X, is called subquadratic. If the sign "is less than or equal to" is replaced by "is more than or equal to" then phi is called superquadratic and if we have "=" instead of " is less than or equal to" in (1) then we say that phi is quadratic function. There are plenty papers devoted to quadratic functions [1], [2], [3] (and references there). In this note some properties of the solutions of (1) will be proved, particularly we will investigate nonpositive solutions of (1). Also interesting question of finding sucient conditions on subquadratic function to be quadratic one will be considered.
8
Content available remote On subsemigroups of the L1/s
Jabłoński W.
Demonstratio Mathematica
|
2006
|
Vol. 39, nr 4
815-823
EN
In this paper we consider subsemigroups of the group L1/s such that the r–th parameter of xs is the function of the remaining ones. Moreover we generalize some results concerning the existence of certain form subsemigroups of the group L1/s.
9
Content available remote On some subsemigroups of the groups L1/s and L1/nieskończoność
Jabłoński W.
Demonstratio Mathematica
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2006
|
Vol. 39, nr 2
305-316
EN
The problem of determination of some class of geometric objects has been reduced about forty years ago to consideration of some subsemigroups of the differential group L1/s (cf. [1] and [6]). Over the last years many papers has been devoted the problem of determining of subsemigroups and subgroups of the group L/s (see among others (2], (3] and (5]-[15]). In this paper we are going to generalize the results from [5], [9] and (13] concerning determination of some form subsemigroups of the group L1/s.
10
Content available remote Iterative equations in p-normes spaces
Żołdak M.
Demonstratio Mathematica
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2006
|
Vol. 39, nr 3
571-578
EN
Let X be a real p-normed, complete space and V be a nonempty closed subset of X. We consider the functional equation.
11
Content available remote A remark on quasiaffine functions
Lewicki M.
Demonstratio Mathematica
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2006
|
Vol. 39, nr 4
743-750
EN
We consider the functional inequality (*) min{f(x), f(y)} is less than or equal to f (rx + (1 - r)y) is less than or equal to max{f(x), f(y)}, where f is a real valued function on a linear space X and r is an element of (0, 1) is fixed. The purpose of the present paper is to investigate connections between functions satisfying inequality (*) and solutions of (*) with r = 1/2. As a conclusions we get, that under some regularity assumptions, function f is of the form f = g o alpha, where alpha : X approaches R is an additive and g : R approaches R is monotone.
12
Content available remote Stability of difference equations generated by parabolic differential functional equations
Ciarski R.
Demonstratio Mathematica
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2005
|
Vol. 38, nr 1
101--117
EN
The aim of this paper is to present a numerical approximation for the initial boundary value problem for quasilinear parabolic differential functional equations. The convergence result is proved for the difference scheme with the property that the difference operators approximating mixed derivatives depend on local properties of coefficients of the differential equation. A numerical example is given.
13
Content available remote On the Sincov functional equation
Piątek B.
Demonstratio Mathematica
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2005
|
Vol. 38, nr 4
875--881
EN
The Riemarm integral, the Hukuhara differences and derivatives will be applied to obtain solutions of the Sincov functional equation.
14
Content available remote On the equation associated with bounded paraconcave entropies
Dudek Z.
Demonstratio Mathematica
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2005
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Vol. 38, nr 2
401--411
EN
A paraconcave entropy function [2] is represented by a pair of two real functions of a real variable satisfying certain natural conditions. The subject of this paper is the functional equation, L(sum j f(pj)) = sum j g(pj)i, that describes equivalence between two representations of a paraconcave entropy function with concave functions f and g satisfying the condition for a bounded entropy. With the use of E-transforms of the functions f and g we reduce the problem of solvability of the equation to the problem ofinjectivity of a certain nonlinear operator denned on the set of concave homeomorphisms of the interval [0,1] onto itself. Additionally, we prove some facts about concavity of the E-transform f.
15
Content available remote On a functional equation related to an automorphism of a unit circle
Kir'ytzkii E.
Demonstratio Mathematica
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2005
|
Vol. 38, nr 1
119--134
EN
In this article the complete description of the decisions of a functional equation f(w(z)) = f(w(0))f(z) is given, where w(z)-automorphism of a unit circle E and the decisions are searched among analytical in E functions. It is established, that research of a given functional equation is closely connected to property of stationary points of automorphism w(z).
16
Content available remote Generalized Euler method for nonlinear first order partial differential functional equations
Kamont Z., Nadolski A.
Demonstratio Mathematica
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2005
|
Vol. 38, nr 4
976-996
EN
Classical solutions of the local Cauchy problem on the Haar pyramid are approximated in the paper by solutions of suitable quasilinear systems of difference equations. The proof of the stability of the difference problem is based on a comparison technique with nonlinear estimates of the Perron type. This new approach to the numerical solving of nonlinear functional differential equations is generated by a quasilinearization method for initial problems. Numerical examples are given.
17
Content available remote Linear approximation and asymptotic expansion associated with the system of functional equations
Long N.
Demonstratio Mathematica
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2004
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Vol. 37, nr 2
349--362
18
Content available remote Abstract variable domain hyperbolic differential equations
Guezane-Lakoud A.
Demonstratio Mathematica
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2004
|
Vol. 37, nr 4
883--892
EN
An abstract problem is studied for a class of linear hyperbolic differential equations with variable domain and non-local boundary conditions. Existence and uniqueness of the strong solution are proved.
19
Content available remote On a composite functional equation
Matkowski J., Okrzesik J.
Demonstratio Mathematica
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2003
|
Vol. 36, nr 3
653--658
EN
We determine all continuous functions f : (0, oo) ->(0,oo) satisfying the functional equation f(xG(f(x)))=f(x)G(f(x)) where G is continuous and strictly increasing function such that 1 e G((0, oo)).
20
Content available remote On applications of a functional equation
Smajdor W.
Opuscula Mathematica
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2001
|
Vol. 21
93-99
EN
We characterize the sine function applying the functional equation [formula].
PL
Przedstawiono charakteryzację funkcji sinus za pomocą równania funkcyjnego [wzór].
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