caa a22 4500 465825087 CHVBK 20180323112147.0 cr unu---uuuuu 170327e19900401xx s 000 0 eng 10.1007/BF01833149 doi (NATIONALLICENCE)springer-10.1007/BF01833149 Tabor J. Department of Mathematics, Pedagogical University of Cracow, Podchorazych, Cracow, Poland aut Quasi-additive functions [Elektronische Daten] [J. Tabor] Summary: Let 0 ⩽ε < 1 and letX, Y be real normed spaces. In this paper we consider the following functional inequality:∥f(x + y) − f(x) − f(y)∥ ⩽ ε min{∥f(x + y)∥, ∥f(x) + f(y)∥} forx, y ∈ R, wheref: X → Y. Mainly continuous solutions are investigated. In the case whereY = R some necessary and some sufficient conditions for this inequality are given. Let 0 ⩽ε <1. The following functional inequality has been considered in [5]:∥f(x + y) − f(x) − f(y)∥ ⩽ ε min{∥f(x + y)∥, ∥f(x) + f(y)∥} forx, y ∈ R, wheref: R → R. It appeared that the solutions of this inequality have properties very similar to those of additive functions (cf. [1], [2], [3]). The inequality under consideration seems to be interesting also because of its physical interpretation (cf. [5]). In this paper we shall consider this inequality in a more general case, wheref is defined on a real normed space and takes its values in another real normed space. The first part of the paper concerns the general case; in the second part we assume that the range off is inR. Birkhäuser Verlag, 1990 Primary 51G05 nationallicence Secondary 11E81, 12K05, 12K10 nationallicence aequationes mathematicae Birkhäuser-Verlag 39/2-3(1990-04-01), 179-197 0001-9054 39:2-3<179 1990 39 10 https://doi.org/10.1007/BF01833149 text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1007/BF01833149 text/html Onlinezugriff via DOI NATIONALLICENCE 100 1- Tabor J. Department of Mathematics, Pedagogical University of Cracow, Podchorazych, Cracow, Poland aut NATIONALLICENCE 773 0- aequationes mathematicae Birkhäuser-Verlag 39/2-3(1990-04-01), 179-197 0001-9054 39:2-3<179 1990 39 10 Metadata rights reserved Springer special CC-BY-NC licence nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-springer