New Types of Continuities in 2-Normed Spaces

Abstract

A sequence (x(n)) of points in a 2-normed space X is statistically quasi-Cauchy if the sequence of difference between successive terms statistically converges to 0. In this paper we mainly study statistical ward continuity where a function f defined on a subset E of X is statistically ward continuous if it preserves statistically quasi-Cauchy sequences of points in E. Some other types of continuities are also discussed, and interesting results related to these kinds of continuities are obtained in 2-normed space setting.