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Keywords:
continuity; $({\mathbf{G_1}},{\mathbf{G_2}})$-continuity; homogeneous; linearity; conditions (NL1) and (NL2); normed space
continuity; $({\mathbf{G_1}},{\mathbf{G_2}})$-continuity; homogeneous; linearity; conditions (NL1) and (NL2); normed space
Summary:
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.
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