introduce gradual banach lattices and hyers stability

The main objective of this article is to introduce gradual normed riesz spaces and their properties. in fact, by adding a property to gradual normed spaces as discussed in reference [20], we have defined the gradual banach lattices. next, we focus on the stability of the supremum-preserving functional equation in these spaces, utilizing the fixed-point theorem to examine the conditions ensuring stability. also, we can verify the stability of various functional equations in these spaces.