On porosity-convergence of real valued sequences

Received: 9.IX.2015, Accepted: 12.V.2016

Abstract. In this paper, we define a new type of convergence called $\overline{p}_{\mu}$-convergence for real valued sequences by using the porosity notion for subsets of natural numbers at infinity. Besides the main properties of $\overline{p}_{\mu}$-convergence we showed that $\overline{p}_{\mu}$-convergence is a regular summability method.

Keywords: Local upper porosity, Porosity of subsets of natural numbers, Porosity convergence

Mathematics Subject Classification (2010): 28A05, 40A05, 54E35, 30D40

Authors:
Maya Altinok, Mersin University, Faculty of Sciences and Arts, Department of Mathematics, Mersin, Turkey
Mehmet Küçükaslan, Mersin University, Faculty of Sciences and Arts, Department of Mathematics, Mersin, Turkey