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 -