The minimal convergence and Cauchy degree of roughness via natural density

In this article, we continue our exploration of the concepts of ?minimal Cauchy degree? and ?minimal convergence degree? for sequences. This investigation was first introduced in [Numer. Funct. Anal. Optim. 22 (1-2) (2001) 199-222] within the context of finite-dimensional normed spaces. However, we now take a broader approach, emphasizing the significance of natural density and infinite-dimensional normed spaces. Throughout our discussion, we extend several existing results from finite-dimensional to infinite-dimensional context under specific conditions. Additionally, we provide compelling examples to illustrate why some well-established results do not hold in the context of infinite-dimensional normed spaces. Finally, we utilize the concept of the Jung cXonstant J in a normed space X to establish connections between statistical Cauchy degrees and statistical convergence degrees of sequences.