Statistical Convergence With Respect to Power Series Method on Time Scales

Abstract

In the present paper, we introduce some new notions, such as convergence in the sense of power series method and strong convergence in the sense of power series method on an arbitrary time scale. Later, with the help of statistical convergence, the notions of PΔ-density, PΔ-statistical convergence, PΔ-statistical Cauchy are defined and investigated their relations. Also, we give the notion of PΔ-uniform integrability for characterization of PΔ-statistical and PΔ-strong convergence.