On α-order λ-statistical convergence and some inclusion theorems in non-Archimedean 2-normed spaces

Abstract

 This paper introduces the notion of α-order λ-statistical convergence over non-Archimedean 2-normed spaces, with K representing a non-trivially valued, complete non-Archimedean field. Further, properties like linearity, uniqueness of limits, and certain properties of α-order λ-statistical convergence sequences, α-order λ-statistical Cauchy sequences are established in non-classical analysis. Some inclusion theorems are proved, and the concepts of α-order λ-statistical limit superior and α-order λ-statistical limit inferior for sequences in non-Archimedean 2-normed spaces are introduced, along with a discussion of related results.