Approximate homomorphisms

Banach space techniques underpinning a theory for nearly additive mappings

“…For more general results in this direction the reader can consult Rassias [81,84], Gajda [37], Isac and Rassias [53], Rassias andŠemrl [86], Gȃvruţa [40], Jung [59] and the surveys of Hyers and Rassias [52] and Forti [36]. It should be noted that most of these results are particular cases of a general result of Forti [33] about stability of functional equations of the form g(F (x, y)) = G(f (x), f (y)).…”

“…See [36,52] for a sound background, and the comments made in the introductory chapter for an overall panorama. The space of Hyers-additive maps acting between (G, ̺) and…”

“…While a unified theory seems to be out of reach by now, the part of the theory involving quasi-normed groups and maps with values in Banach spaces seems to be ripe with these pages. We hasten to alert the reader that this paper can by no means be considered a survey, although it contains occasional historical comments; two excellent survey papers are [36,52]. …”

“…To support this assertion it is enough to peruse the survey articles [36,52] In fact, both worlds constitute two faces of the same coin. In this spirit, the purpose of this paper is to progress towards a global understanding of the problem, and we shall do so by developing a theory of vector-valued nearly additive mappings on semigroups.…”

Hyers-Ulam stability of derivations on proper Jordan CQ*-algebras

“…In 1994, a generalization of Rassias' Theorem was obtained by Găvruta [5]. Since then, several stability problems for various functional equations have been investigated by numerous mathematicians (see [6][7][8][9][10][11][12][13][14][15][16][17][18][19][20][21][22][23][24][25], M Eshaghi Gordji, unpublished work).…”