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- Title
Lambda-Statistical Convergence in Paranormed Spaces over Non-Archimedean Fields.
- Authors
Saranya, N.; Suja, K.
- Abstract
The objective of this paper is to investigate the concept of λ-statistical convergence, λ-statistically Cauchy sequences, and ideal statistically pre-Cauchy sequences in non-Archimedean paranormed spaces. Here, λ = (λn) is a nondecreasing sequence that tends to ∞, with the properties λn+1 ≤ λn + 1 and λ1 = 1. The study includes proving significant properties of λ-statistical convergence in paranormed spaces and establishing criteria for λ-statistical convergence and λ-statistically Cauchy sequences. The implications of these concepts are discussed in the framework of non-Archimedean fields. Paranormed spaces are considered to have more general properties than normed spaces. The paper also introduces the concept of ideal statistically pre-Cauchy sequences and proves that ideal statistical convergence implies ideal statistical pre-Cauchy behavior in paranormed spaces over non-Archimedean fields. "The field K is assumed to be complete, non-trivially valued, and non-Archimedean field throughout the article."
- Subjects
CAUCHY sequences; SPATIAL behavior
- Publication
IAENG International Journal of Applied Mathematics, 2023, Vol 53, Issue 3, p1028
- ISSN
1992-9978
- Publication type
Article