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Remarks on: "Oscillation criteria for second-order functional difference equation with neutral terms" [Demonstratio Math. 41 (2008)]

Karpuz B.

Demonstratio Mathematica

2009

Vol. 42, nr 3

549-551

In this paper, we show that the paper mentioned in the title includes some wrong results. We also provide a counter example.

On Some Special Morphisms Between Groups and Algebras

Fidytek I.

Scientific Issues of Jan Długosz University in Częstochowa. Mathematics

2006

Vol. 11

17-40

Study of some functional equations related to some algebras of matrices

Akkouchi M., Rhali M.

Demonstratio Mathematica

2005

Vol. 38, nr 3

611--622

Let K be the real or complex field. Let 1 < n < p be two positive integers. We denote Mp(K) the usual algebra of p x p-matrices. Let An be an n- dimensional subalgebra of Mp(K). Then there exists an injective linear mapping A : Kn- Mp(K) such that A^") = An' Therefore K" may be equipped with a product denoted * such that (Kn, +,*) is an associative algebra. The aim of this paper is to investigate the general solutions of the functional equation: f(x*y) = f(x) f(y), and its Pexider form f(x*y) = g(x) h(y), for all x, y in Kn, where f,g, h: Kn - K are unknown functions. This work is inspired by the paper [2].

On the stability of a mean value type functional equation

Jung S., Sahoo P.

Demonstratio Mathematica

2000

Vol. 33, nr 4

793-796

In this paper, we prove the stability results of a mean value type functional equation, namely f (x) - g{y) = (x - y)h(x 4- y) which arises from the mean value theorem.

Extension theorems for the Matkowski-Suto problem

Daroczy Z., Maksa G., Pales Z.

Demonstratio Mathematica

2000

Vol. 33, nr 3

547-556

A localization principle for classes of means

Berrone L.

Demonstratio Mathematica

2000

Vol. 33, nr 3

557-566

Several families of continuous means defined on a square I x I have the remarkable property of being entirely determined when their values in an arbitrary small neigborhood of the diagonal {(x,x) : x G 1} of the square are known. Some examples are given of application of this property in solving functional equations.

On solutions of some system of functional equations

Midura S.

Demonstratio Mathematica

1998

Vol. 31, nr 2

299-304