In an unpublished paper A. G\"ulc\"u introduced a generalized
notion of strong summation termed "strong A-summability in the
wide sense". We investigate this notion and clarify some points
left unclear by the initial paper of G\"ulc\"u. We settle
integrability of the $A$-distribution function under condition of
finitely strong A-summability in the wide sense and analyze
necessity of conditions to conclude finitely strong A-summability
in the wide sense from $A$-distributional summability. In
particular, we prove a sharp direct theorem as well as its
corresponding converse theorem to describe connection of these
notions. We also clarify connection of finitely strong
A-summability in the wide sense and usual $A$-summability and
compute the sum of a sequence from information about its
generalized $A$-strong summation or its $A$- distribution. The
paper ends with comments on the original work of A. G\"ulc\"u.\