Modulated convergence: a deferred approach

Abstract

In this paper, we further develop the study of the interplay between statistical and strong Ces & agrave;ro convergence modulated by a modulus function, as initiated in the papers by Saavedra et al. and Romero de la Rosa. Our focus is on the deferred versions of these convergence methods. We show that the fundamental relationship between them remains valid in the deferred context, thereby extending and refining the results obtained by Bhardwaj and Gupta, and Belen and Y & imath;ld & imath;r & imath;m.