Rough ideal convergence of sequences in gradual normed linear spaces

Abstract

For a non-empty set X, an ideal I represents a family of subsets of X that is closed under taking finite unions and subsets of its elements. Considering X = N, in the present study, we set forth with the new concept of rough I and I & lowast;-convergence in gradual normed linear spaces (GNLS). We produce significant results that present several fundamental features of the notions utilizing Ir(G) and I & lowast;,r(G)-limit set. In the end, we investigate their interrelationships and establish a necessary and sufficient condition for the equivalency of the two notions.