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Fischer-Muszély additivity on Abelian groups

Ger R.

Annales Societatis Mathematicae Polonae. Seria 1: Commentationes Mathematicae

2004

Vol. 44, nr spec.

83-96

A description of a general solution f : X -> Y mapping a commutative group (X, +) into a real normed linear space (Y, || o ||) of the functional equation [formula] is given in terms of isometrics and additive mappings. Several results describing the solutions of this equation that were obtained earlier under some alternative assumptions regarding the domains, ranges and//or by imposing some regularity upon the map f become special cases of our main result. To gain a proper proof tool we have also established an improvement of E. Berz's [4] representation theorem for sublinear functionals on Abelian groups.

σ-core for real bounded sequences

Yardimci S.

Demonstratio Mathematica

2002

Vol. 35, nr 1

111-116

In this paper, using the idea that Choudhary used, we extend the previously known results for σ-core of real bounded sequences.