TY - JOUR
ID - 848
TI - Hyperstability of some functional equation on restricted domain: direct and fixed point methods
JO - Bulletin of the Iranian Mathematical Society
JA - BIMS
LA - en
SN - 1017-060X
AU - Bahyrycz, A.
AD - AGH University of Science and Technology, Faculty of Applied Mathematics, Mickiewicza 30, 30-059 Krakow, Poland.
Y1 - 2016
PY - 2016
VL - 42
IS - 4
SP - 959
EP - 974
KW - Hyperstability
KW - linear equation
KW - quadratic equation
KW - p-Wright affine function
KW - fixed point theorem
DO -
N2 - The study of stability problems of functional equations was motivated by a question of S.M. Ulam asked in 1940. The first result giving answer to this question is due to D.H. Hyers. Subsequently, his result was extended and generalized in several ways.We prove some hyperstability results for the equation g(ax+by)+g(cx+dy)=Ag(x)+Bg(y)on restricted domain. Namely, we show, under some weak natural assumptions, that functions satisfying the above equation approximately (in some sense) must be actually solutions to it.
UR - http://bims.iranjournals.ir/article_848.html
L1 - http://bims.iranjournals.ir/article_848_f70737eade2a159a95d98ee8c93435c2.pdf
ER -