Title of article :
On the Space of Real Valued Statistically Convergent Sequences
Author/Authors :
Sohooly, Y. Islamic Azad University Shiraz Branch, Shiraz , Jahedi, Khadijeh Islamic Azad University Shiraz Branch, Shiraz , Alikhani-Koopaei, A. Pennsylvania State University, USA
Abstract :
The aim of this paper is to introduce an equivalence relation on the space of real valued statistically convergence sequences, Cst, and an inner product on the set of its equivalence classes. We equip Cst with the induced J- metric, dJ , by the given inner product. We prove that Cst is a complete J-metric space. We also show that the space of all real valued convergent sequences is a dense subspace of (Cst, dJ ).
Keywords :
Natural density of sets , statistically convergence , equivalence relation , quotient space
Journal title :
Journal of Mathematical Extension(IJME)
