Strongly Summable Bivariate Measurable Functions of Weight g

Year 2020, Volume: 15 Issue: 1, 80 - 89, 31.05.2020

Rabia Savas

https://doi.org/10.29233/sdufeffd.694376

Cited By: 1

Abstract

In 1965 Borwein presented the concept of strongly summable single valued functions. Using Borwein's results, in 2019 Patterson et all. introduced the notion of multidimensional linear functions connected with double strongly Cesaro summability theory. The aim of this study is to extend Patterson et all's results to strongly summable bivariate functions with respect to weight of g. To achieve this by considering a real valued non-negative bivariate measurable function defined on the interval (1,∞)×(1,∞) the concepts of double [W_(λ,μ)^g ]_f -strongly summable and [S_(λ,μ)^g ]_f-double statistical convergence of weight g will be introduced, where g:[0,∞)×[0,∞)→[0,∞) such that g(x_m,x_n )→∞ as x_m→∞ and x_n→∞. Also g is factorable. In addition, the relationship between these two concepts will be examined and some algebraic characterization of real valued lebesgue measurable bivariate functions will be also presented.

Keywords

Statistical convergence functions of two variables, real valued Lebesgue measurable function, strong summability, weight g

g Ağırlıklı Kuvvetli Toplanabilir İki Değişkenli Ölçülebilir Fonksiyonlar

Abstract

1965 yılında Borwein tek değişkenli kuvvetli toplanabilir fonksiyonları sunmuştur. Borwein'nin sonuçlarını kullanarak 2019 yılında Patterson ve diğerleri çift kuvvetli Cesaro toplanabilme teorisi ile bağlantılı olarak iki boyutlu lineer fonksiyonları tanımlamıştır. Bu makalenin amacı Patterson ve diğerlerinin sonuçlarının g ağırlığı ile ilişkili olarak kuvvetli toplanabilir iki değişkenli ölçülebilir fonksiyonlara genelleştirmektir. Bunu elde etmek için (1,∞)×(1,∞) aralığında tanımlı negatif olmayan reel değerli iki değişkenli ölçülebilir fonksiyonlar göz önüne alınarak eğer x_m→∞ ve x_n→∞ iken g(x_m,x_n )→∞ olacak şekilde g:[0,∞)×[0,∞)→[0,∞) ağırlıklı çift [W_(λ,μ)^g ]_f-kuvvetli toplanabilir ve [S_(λ,μ)^g ]_f-çift istatistiksel yakınsaklık kavramları sunulacaktır. Ayrıca, g fonksiyonu çarpanlarına ayrılabilir. Buna ek olarak, bu iki kavram arasındaki ilişki incelenecek ve reel değerli Lebesgue anlamında ölçülebilir iki değişkenli fonksiyonların bazı cebirsel özellikleri de verilecektir.

Keywords

İki değişkenli fonksiyonların istatistiksel yakınsaklığı, reel değerli Lebesgue ölçülebilir fonksiyonlar, kuvvetli toplanabilme, g ağırlık

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