Statistical p-convergence in lattice-normed Riesz spaces

2022/04/22 by Aydın, Abdullah, Yapalı, Reha, Korkmaz, Erdal
#FOS: Mathematics #Functional Analysis (math.FA)

paper · doi:10.48550/arxiv.2204.10499

Abstract

A sequence (x_n) in a lattice-normed space (X,p,E) is statistical p-convergent to x∈ X if there exists a statistical p-decreasing sequence q\stpd 0 with an index set K such that δ(K)=1 and p(x_nk-x)≤ q_nk for every n_k∈ K. This convergence has been investigated recently for (X,p,E)=(E,|⋅|,E) under the name of statistical order convergence and under the name of statistical multiplicative order convergence, and also, for taking E as a locally solid Riesz space under the names statistically unbounded τ-convergence and statistically multiplicative convergence. In this paper, we study the general properties of statistical p-convergence.

Related

• Statistically unbounded p-convergence in lattice-normed Riesz spaces
• The statistically unbounded τ-convergence on locally solid Riesz spaces
• Statistical order convergence of operators on Riesz Spaces
• Statistical unbounded convergence in Banach lattices
• Statistical convergence of nets in Riesz spaces