TY - JOUR
ID - 72
TI - stability of the quadratic functional equation
JO - International Journal of Nonlinear Analysis and Applications
JA - IJNAA
LA - en
SN -
AU - Elqorachi, E.
AU - Manar, Y.
AU - Rassias, Th. M.
AD - Department of Mathematics, Faculty of Sciences, University Ibn Zohr, Agadir, Morocco
AD - Department of Mathematics, National Technical University of Athens, Zografou Campus, 15780, Athens, Greece
Y1 - 2010
PY - 2010
VL - 1
IS - 2
SP - 26
EP - 35
KW - Hyers-Ulam-Rassias stability
KW - quadratic functional equation
DO - 10.22075/ijnaa.2010.72
N2 - In the present paper a solution of the generalized quadratic functional equation$$f(kx+ y)+f(kx+sigma(y))=2k^{2}f(x)+2f(y),phantom{+} x,yin{E}$$
is given where $sigma$ is an involution of the normed space $E$ and $k$ is a fixed positive integer. Furthermore we investigate the Hyers-Ulam-Rassias stability of the functional equation. The Hyers-Ulam stability on unbounded domains is also studied. Applications of the results for the asymptotic behavior of the generalized quadratic functional equation are provided.
UR - https://ijnaa.semnan.ac.ir/article_72.html
L1 - https://ijnaa.semnan.ac.ir/article_72_80bd73337686e609bb56f0fac56e6130.pdf
ER -