REGULAR INTEGRAL TRANSFORMATIONS ON TIME SCALES AND GENERALIZED STATISTICAL CONVERGENCE

Abstract

In this work, using regular integral transformations on time scales,
we generalize the concept of statistical convergence. This enables us not only
to unify discrete and continuous cases known in the literature but also to
derive new convergence methods with choices of appropriate transformations
and time scales. This is a continuation of our earlier work and includes many
new methods. We obtain sufficient conditions for regularity of kernel functions
on time scales and also we prove a characterization theorem for the generalized
statistical convergence. At the end of the paper we display some applications
and special cases of our results.