New results in gradual normed linear spaces in light of generalized statistical convergence via ideal

Abstract

This article introduces the novel concept of rough I- statistical convergence of order alpha in gradual normed linear spaces (GNLS). The paper presents noteworthy findings utilizing the I-st (r ,alpha )(G)- limit set, which exhibits several fundamental properties of the concept. Moreover, a necessary and sufficient condition I-st (r ,alpha )(G)-convergence G ) - convergence of a sequence in a GNLS is established.