Wijsman summability through Orlicz Function Sequences

Year 2024, Volume: 12 Issue: 2, 100 - 105, 30.12.2024

Erdal Bayram

https://doi.org/10.18586/msufbd.1551410

Abstract

The Wijsman convergence is a type of convergence for sequences of closed sets in metric spaces, utilizing the distance from a point to a set. This study introduces a new sequence space by defining a summability concept for sequences of closed sets in the Wijsman sense, using sequences of Orlicz functions. Various inclusion theorems related to the space of Wijsman statistically convergent sequences of sets have been presented, considering different parameters used in the definition of this set sequence space. Additionally, in the obtained results, a concept of density has been employed using weight functions instead of asymptotic density.

Keywords

Density, Orlicz function, Statistical convergence, Wijsman convergence

Orlicz Fonksiyon Dizileri İle Wijsman Toplanabilirlik

Abstract

Wijsman yakınsaması, metrik uzaylarda kapalı küme dizileri için bir yakınsama türüdür ve bir noktanın bir kümeye olan uzaklığını kullanır. Bu çalışmada, Orlicz fonksiyonlarının dizileri kullanılarak, Wijsman anlamında kapalı kümeler dizileri için bir toplanabilirlik kavramı tanımlanarak yeni bir dizi uzayı önerilmiştir. Bu küme dizileri uzayının tanımlanmasında kullanılan parametrelerin farklılaşması durumunda veya Wijsman istatistiksel yakınsak küme dizilerinin uzayıyla ilişkili çeşitli kapsama teoremleri sunulmuştur. Ayrıca, elde edilen sonuçlarda, asimptotik yoğunluk yerine ağırlık fonksiyonları kullanılarak elde edilen bir yoğunluk kavramı kullanılmıştır.

Keywords

Yoğunluk, Orlicz fonksiyonu, İstatistiksel yakınsaklık, Wijsman yakınsaklık

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