Geodesic
On some consequences of a generalized continuity
Archivum mathematicum, Tome 50 (2014) no. 2, pp. 107-114 Cet article a éte moissonné depuis la source Czech Digital Mathematics Library

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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}) $-continuity) and examine some of its consequences in respect of usual continuity and linearity of the operators between two normed linear spaces.
In normed linear space settings, modifying the sequential definition of continuity of an operator by replacing the usual limit "$\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.
DOI : 10.5817/AM2014-2-107
Classification : 40C05, 47L05
Keywords: continuity; $({\mathbf{G_1}}, {\mathbf{G_2}})$-continuity; homogeneous; linearity; conditions (NL1) and (NL2); normed space 
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Das, Pratulananda; Savas, Ekrem. On some consequences of a generalized continuity. Archivum mathematicum, Tome 50 (2014) no. 2, pp. 107-114. doi: 10.5817/AM2014-2-107

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