On some consequences of a generalized continuity

Abstract

In normed linear space settings, modifying the sequential definition of continuity of an operator by replacing the usual limit "$\lim $" with arbitrary linear regular summability methods $\bf {G}$ we consider the notion of a generalized continuity ($(\bf {G_1}, \bf {G_2}) $-continuity) and examine some of its consequences in respect of usual continuity and linearity of the operators between two normed linear spaces.