Address:
P. Das, Department of Mathematics, Jadavpur University, Kolkata-700032, West Bengal, India
E. savas, Istanbul Ticaret University, Department of Mathematics, Üsküdar-Istanbul, Turkey
E-mail:
pratulananda@yahoo.co.in
ekremsavas@yahoo.com
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.
AMSclassification: primary 46B05; secondary 40C05.
Keywords: continuity, ({\mathbf{G_1}},{\mathbf{G_2}})-continuity, homogeneous, linearity, conditions (NL1) and (NL2), normed space.
DOI: 10.5817/AM2014-2-107