Bektaş, ÇiğdemÖzçelik, Emine2021-02-212021-02-2120192667-7814https://dergipark.org.tr/tr/download/article-file/587424https://hdl.handle.net/20.500.12868/1422In this study, we introduce the concepts of strongly  ($\Delta ^{m}$,p)-Cesàro summability,  $\Delta ^{m}-statistical Cauchy sequence and  $\Delta ^{m}-statistical convergence in a paronormed space. We give some certain properties of these concepts and some inclusion relations between them.In this study, we introduce the concepts of strongly ? ? m ? ,p -Cesàro summability, m ? -statistical Cauchy sequence and m ? -statistical convergence in a paronormed space. We give some certain properties of these concepts and some inclusion relations between them. Fast [1] and Steinhaus [2] introduced the concept of statistical convergence for sequences of real numbers. Several authors studied this concept with related topics [3-5]. The asymptotic density of K N ? is defined as, ? ? n 1 (K) lim k n : k K ?? n ? ? ? ? where K be a subset of the set of natural numbers N and denoted by ? ?K?. . indicates the cardinality of the enclosed set. A sequence ?xk ? is called statistically covergent to L provided that ? k ? n 1 lim k n ? L 0 ?? n ? ? ? ? ? ? for each ?? 0 . It is denoted by lim k k st x L ?? ? ? . A sequence ??k ? is called statistically Cauchy sequence provided that there exist a number N N( ) ? ? such thateninfo:eu-repo/semantics/openAccessStatistical convergencestatistical Cauchyparanormed spaceStatistical convergencestatistical Cauchyparanormed spacedifference sequenceArticle114047