Applications of Relations and Relators in the
Extensions of Stability Theorems for Homogeneous and Additive Functions
Applications of Relations and Relators in the Extensions of Stability Theorems for Homogeneous and Additive Functions
Institute of Mathematics, University of Debrecen,
H-4010 Debrecen, Pf. 12,
By working out an appropriate technique of relations and relators and extending the ideas of the direct methods of Z. Gajda and R. Ger, we prove some generalizations of the stability theorems of D. H. Hyers, T. Aoki, Th. M. Rassias and P. Găvruţă in terms of the existence and unicity of 2-homogeneous and additive approximate selections of generalized subadditive relations of semigroups to vector relator spaces. Thus, we obtain generalizations not only of the selection theorems of Z. Gajda and R. Ger, but also those of the present author.
Full Text PDF: