A NOTE ON THE GENERALISED HYPERSTABILITY OF THE GENERAL LINEAR EQUATION

作者：Aiemsomboon Laddawan; Sintunavarat Wutiphol^*

来源：Bulletin of the Australian Mathematical Society, 2017, 96(2): 263-273.

DOI：10.1017/S0004972717000569

• fixed point
• generalised hyperstability
• general linear equation

Let X and Y be two normed spaces over fields F and K, respectively. We prove new generalised hyperstability results for the general linear equation of the form g(ax + by) = Ag(x) + Bg(y), where g : X -> Y is a mapping and a; b is an element of F, A; B is an element of K\{0}, using a modification of the method of Brzdek ['Stability of additivity and fixed point methods', Fixed Point Theory Appl. 2013 (2013), Art. ID 285, 9 pages]. The hyperstability results of Piszczek ['Hyperstability of the general linear functional equation', Bull. Korean Math. Soc. 52 ( 2015), 1827-1838] can be derived from our main result.

• 出版日期2017-10