A Study on (𝝍,𝝋) Weakly Contractive Mapping via (𝓕,𝒉) Upper Class

Öz

Branciari reorganized the notion of metric to attain a novel distance function by replacing the triangular inequality with the quadrilateral inequality. The reorganized metric function was said rectangular metric in some resources, or general metric in some others. Ansari introduced a more general function so-called upper class. Inspired and motivated by this facts, we give an extansion of weakly contractive mapping via upper class type II in the setting of Branciari metric space. An application is given here to prove new fixed point results for graphic weakly contractive mappings in Branciari metric space endowed with a graph. Moreover, we derive an example in support of our main results.

Anahtar Kelimeler

• fixed point
• Branciari metric space
• (F,h) Upper class

(𝓕,𝒉) Üst Sınıfı Aracılığıyla (𝝍,𝝋) Zayıf Büzülme Dönüşümleri Üzerine Bir Çalışma

Öz

Branciari, metrik uzaydaki iki terimli üçgen eşitsizliğini üç terimli dörtgen eşitsizliğiyle yer değiştirerek yeni bir mesafe fonksiyonu oluşturmak için metrik kavramını yeniden yapılandırdı. Tanımlanan bu fonksiyon literatürde dikdörtgensel metrik ya da genelleştirilmiş metrik olarak adlandırılır. Ansari tarafından ortaya konulan üst sınıf dönüşümü temel alınarak Branciari metrik uzayında üst sınıf tip II aracılığıyla zayıf büzülmeli dönüşümlerin bir genellemesi verildi. Sonraki aşamada ise bir çizge vasıtasıyla Branciari metrik uzayında grafik zayıf büzülmeli dönüşümler için yeni sabit nokta sonuçlarını ispat etmek amacıyla burada bir uygulama verildi. Son olarak çalışılan dönüşüm için ana sonuçlarımızı destekleyen bir örnek gösterildi.

Anahtar Kelimeler

• sabit nokta
• Branciari metrik uzayı
• (F,h) Üst Sınıfı

Kaynakça

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