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On asymmetric I and I∗-divergence

Ghosal S., Pal S. K.

Demonstratio Mathematica

2013

Vol. 46, nr 1

137--147

In this paper we introduce and study the concepts of I-divergence and I∗-divergence of sequences as well as double sequences in an asymmetric metric spaces. We investigate the interrelationship between I-divergence and I∗-divergence and show that they are equivalent under some condition and prove some basic properties of these concepts.

I-uniform continuity and I-uniform boundedness of a function

Ghosal S.

Demonstratio Mathematica

2012

Vol. 45, nr 4

887-894

The concepts of I-convergence and I-Cauchy condition are a generalization of statistical convergence and statistical Cauchy conditions and are dependent on the notion of the ideal I of subsets of the set N of positive integers. In this paper, we shall introduce two new notions of I-uniform continuity and I-uniform boundedness of a function with values in R or in a metric space and then study their basic properties.