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The stability of a generalized quadratic functional equation

Grabiec, Artur (1997)

In the paper we consider the stability of the functional equation f ( x + y) + f ( x - y) + ||f ( x + y) - f (x - y)||u = 2f(x) + 2f(y), where f : G —> X, X is a normed space, u ϵ X such that ||u|| ≥ 1 and ||u|| ≠ 3 is ...

Quasi-linear mappings

Tabor, Józef (1997)

Let E[1], E[2] be real normed spaces and let ε ϵ [0,1). The paper deals with the system of inequalities || f(x + y) - f(x) - f(y)|| ≤ ε min{||f(x + y)||,||f(x) + f(y)||} for x , y ϵ E[1], II f(αx) - αf(x)|| ≤ ε min ...

Generalized convex sets

Krzyszkowski, Janusz (1997)

In this paper we shall present a definition of convex set with respect to a two-parameter family of functions. It appears that these sets have some properties like convex sets in the usual sense.

On the convergence of singular integrals of vector-valued functions

Siudut, Stanisław (1997)

The pointwise convergence of abstract singular convolution integrals K(•,v) * f (x - •) depending on two parameters x,v (x ϵ R, v belongs to a metric space E) is studied. The convergence of the parameters is restricted to ...

Sur un développement de la valeur moyenne

Wachnicki, Eugeniusz (1997)

Remarks on real-valued quasi-isometries

Chmieliński, Jacek (1997)

In this paper we consider the class of solutions of the functional inequality | |f(x) - f( y)| - |x – y| | ≤ ε ϵ min{|f(x) - f(y)|,|x - y|}, x, y ϵ R where f : IR -> IR is the unknown function and ε ϵ [0,1). The two ...

On bounded solutions of a generalized Schilling's problem

Ciepliński, Krzysztof (1997)

In this note we prove that, under some assumptions on a, b, c, h, g and Q, the zero function is the only solution φ : R → R of the functional equation φ(g(x)) = a(x)φ(h(x)) + b(x)φ(h[-1](x)) + c(x)φ(x), bounded in a ...

Singular solutions of some nonlinear singular partial differential equations

Pliś, Maria E. (1997)

In this paper a family of formal solutions of the Laplace-Beltrami equation is constructed and the convergence of these formal series is proved by finding the majorant convergent series.