On some consequences of a generalized continuity

Pratulananda Das; Ekrem Savaş

Archivum Mathematicum (2014)

  • Volume: 050, Issue: 2, page 107-114
  • ISSN: 0044-8753

Abstract

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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 𝐆 we consider the notion of a generalized continuity ( ( 𝐆 1 , 𝐆 2 ) -continuity) and examine some of its consequences in respect of usual continuity and linearity of the operators between two normed linear spaces.

How to cite

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Das, Pratulananda, and Savaş, Ekrem. "On some consequences of a generalized continuity." Archivum Mathematicum 050.2 (2014): 107-114. <http://eudml.org/doc/261144>.

@article{Das2014,
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.},
author = {Das, Pratulananda, Savaş, Ekrem},
journal = {Archivum Mathematicum},
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},
language = {eng},
number = {2},
pages = {107-114},
publisher = {Department of Mathematics, Faculty of Science of Masaryk University, Brno},
title = {On some consequences of a generalized continuity},
url = {http://eudml.org/doc/261144},
volume = {050},
year = {2014},
}

TY - JOUR
AU - Das, Pratulananda
AU - Savaş, Ekrem
TI - On some consequences of a generalized continuity
JO - Archivum Mathematicum
PY - 2014
PB - Department of Mathematics, Faculty of Science of Masaryk University, Brno
VL - 050
IS - 2
SP - 107
EP - 114
AB - 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.
LA - eng
KW - 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
UR - http://eudml.org/doc/261144
ER -

References

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