Das, PratulanandaSavaş, Ekrem2020-11-212020-11-2120170139-9918https://doi.org/10.1515/ms-2017-0021https://hdl.handle.net/11467/3549We introduce a convergence of weight g: ? ? [0, ?) where g(n) ? ? and n/g(n) ? 0 with respect to a summability matrix method A for sequences (which generalizes the notion of A-convergence of order ?, 0 < ? ? 1 [BOCCUTO, A. - DAS, P.: On matrix methods of convergence of order (?) in (?)-groups, Filomat 29 (2015), 2069-2077] in a (?)-group. We prove some basic results including a Cauchy-type criterion. Finally a closedness result for the space of such convergent sequences is proved. © 2017 Mathematical Institute Slovak Academy of Sciences.eninfo:eu-repo/semantics/closedAccess(?)-groupA density of weight gAg-convergencesummability matrixArticle674929938Q4WOS:000407235100010Q22-s2.0-8502665085410.1515/ms-2017-0021