A Study On and#955; Ideal Statistical Convergence in Non Archimedean Fields

Abstract

The main objective of this work is to investigate essential properties of statistical newlineconvergence sequence in non-Archimedean fields. Statistical convergence finds numerous newlineapplications in various mathematical fields such as approximation theory, measure theory, newlineprobability theory, trigonometric series, and number theory. newlineThe theory of summability over valued fields holds significant importance in newlinemathematics, with applications ranging from analytic continuation and quantum newlinemechanics to probability theory, Fourier analysis, approximation theory, and fixed-point newlinetheory. This work aims to provide certain characterizations of and#955; - I -statistical convergence newlineof sequences and and#955; - I -statistical Cauchy sequences, along with establishing relevant newlineresults in non-Archimedean fields. newlineThe concept of statistical convergence play a pivotal role in summability theory newlineand functional analysis, offering various applications in analysis and applied mathematics. newlineDefinitions of and#955; - I -statistical convergence of sequences and statistical Mand#955; -summability newlinemethod are provided, and several related theorems are proven in non-Archimedean fields. newlineNecessary and sufficient conditions are derived, and inclusion theorems are established newlineconcerning the statistical limit superior and statistical limit inferior in a non-Archimedean newlineL -fuzzy normed space in such fields K newline