# On some consequences of a generalized continuity

## Pratulananda Das and Ekrem Savas

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