(V, ?)-ORDER SUMMABLE IN RIESZ SPACES - Aydin, Abdullah; Cinar, Muhammed; Et, Mikail (Editura Bibliotheca-Bibliotheca Publ House, 2021)
Statistical convergence is an active area, and it appears in a wide variety of topics. However, it has not been studied extensively in Riesz spaces. There are a few studies about the statistical convergence on Riesz spaces, but they only focus on the relationship between statistical and order convergences of sequences in Riesz spaces. In this paper, we introduce the notion of (V, lambda)-order summable by using the concept of lambda-statistical monotone and the lambda-statistical order convergent sequences in Riesz spaces. Moreover, we give some relations between (V, lambda)-order summable and lambda-statistical order convergence.
Keywords: (V, lambda)-order summable; lambda-statistical monotone; lambda-statistical order convergence; statistical convergence; Riesz space; order convergence