Lipschitz Criteria for Bi-Quadratic Functional Equations

Abstract

Abstract. In this paper, we establish approximation of bi-quadratic functional equations in Lipschitz spaces.

Stability of multi-cubic functions via Lipschitz criteria

“…Czerwik and Dlutek [12] investigated the stability of the quadratic functional equations in Lipschitz spaces. The author established the stability of quadratic, cubic, and quartic functional equations in Lipschitz spaces [13,14,15,16,17,18]. Cieplinski confirmed the generalized Hyers-Ulam stability of multi-quadratic mappings in Banach spaces and completed non-Archimedean spaces [19] (see also [20,21,22]).…”

Approximate tri-quadratic functional equations via Lipschitz conditions

“…The Lipschitz stability type problems for some functional equations were also studied by Tabor, see [12], [13]. In Lipschitz spaces we investigated the stability of cubic functional equations in [2] and the stability of quartic functional equations in [7] (see also [6], [5]). The stability problem for the quadratic and bi-quadratic functional equation has been studied by many mathematicians under various degrees of generality imposed on the equation or on the underlying space; see, for example, [3], [4], [10], [9] and the references therein.…”

“…The stability problem for the quadratic and bi-quadratic functional equation has been studied by many mathematicians under various degrees of generality imposed on the equation or on the underlying space; see, for example, [3], [4], [10], [9] and the references therein. We obtained Lipschitz criteria for bi-quadratic functional equations in Lipschitz spaces in [8].…”