N-Normlu uzaylarda ıstatistiksel ve λ-ıstatistiksel yakinsaklik uzerine

Abstract

Bu tez ¸calı¸sması altı b¨olu¨mden olu¸smaktadır. Birinci b¨olu¨mde, ¸calı¸stıg˘ımız tez konusu ile ilgili kavramların tarihsel geli¸siminden

bahsedildi. I˙kinci b¨olu¨mde, ¸calı¸smamız i¸cin temel te¸skil eden tanım, notasyon, ¨ornek

ve teoremler verildi. U¨ ¸cu¨ncu¨ b¨olu¨mde, 2-normlu uzaylarla ilgili tanım, kavram ve teo-

remler verilerek 2-normlu uzaylarla ilgili bazı ¨onemli ¨ozellikler incelendi. D¨ordu¨ncu¨ b¨olu¨mde, n-normlu uzaylarla ilgili tanım, kavram ve teoremler verilerek n-normlu uza- ylarla ilgili bazı ¨onemli ¨ozellikler incelendi. Be¸s˙ıncı˙ b¨olu¨mde, n-normlu uzaylarda is- tatistiksel yakınsaklık kavramı tanıtılarak bu kavramın bazı ¨onemli ¨ozellikleri, ilgili teoremler ve ispatları ile bazı ¨ornekler verildi. Ayrıca, n-normlu uzaylarda istatis- tiksel Cauchy dizi kavramı ve bu kavramın istatistiksel yakınsaklık ile ili¸skisi ince- lendi. Altıncı b¨olu¨mde, n-normlu uzaylarda λ-istatistiksel yakınsaklık kavramı ve (C, 1)-toplanabilme ve kuvvetli (V, λ)-toplanabilme kavramları verilerek aralarındaki ili¸skiler incelendi.

This thesis consists of six chapters. In the first chapter, historical development of re- lated notions of the thesis subject was mentioned. In the second chapter, some basic definitions, notions, examples and theorems related to study were given. In the third chapter, definitions, concepts, and theorems related to 2-normed spaces were given and some important properties about 2-normed spaces were examined. In the fourth chapter, the concepts, definitions and theorems related to n-normed spaces were given and some important properties about n-normed spaces were investigated. In the five chapter, introducing the concept of statistical convergent in n-normed spaces, some properties, theorems with proofs and some examples of this concept were given. Also, the concept of Cauchy sequence in n-normed spaces was defined and relationships be- tween this concept and statistical convergent was examined. In the six chapter, the concepts of λ-statistical convergent, (C, 1)-summability and (V, λ)-summability were given and relationships between them were investigated.