On Some Fixed Curves in Sb- Metric Spaces

Abstract

In this paper, we mention new results to the fixed-figure problem on Sb- metric spaces. Especially, we emphasize Cassini curve and Appolonius circle. To do this, first of all we give the new notions of Moradi-type Cu1u2- Sb-contraction, Geraghty-type Cu1u2- Sb-contraction, Skof-type Cu1u2- Sb-contraction, Moradi-type Au1u2- Sb-contraction, Geraghty-type Au1u2- Sb-contraction, Skoftype Au1u2- Sb-contraction. With the help of these notions, we obtain some fixed-Cassini curve and fixed-Apollonius circle theorems on Sb- metric spaces.

Keywords

• Sb-metrik spaces
• Cassini curve
• Apollonius circle
• fixed-figure
• contraction.

Sb-Metrik Uzaylarda Bazı Sabit Eğriler Üzerine

Abstract

Bu çalışmada, Sb - metrik uzaylarda sabit figüre problemleri için yeni çözümlerden bahsedilecektir. Özellikle, Cassini Eğrisi ve Apoollonius çemberi üzerinde durulacaktır. Bunun için ilk olarak Moradi tipinde Cu1u2-Sb -daralma, Geraghty tipinde Cu1u2-Sb -daralma, Skof tipinde Cu1u2-Sb -daralma, Moradi tipinde Au1u2-Sb -daralma, Geraghty tipinde Au1u2-Sb -daralma, Skof tipinde Au1u2-Sb -daralma kavramları verilecektir. Bu kavramlar yardımı ile - metrik uzaylar üzerinde sabit Cassini eğrisi ve sabit Apollonius çemberi teoremleri elde edilecektir.

Keywords

• Sb-metrik uzay
• Cassini eğrisi
• Apollonius çemberi
• sabit figüre
• daralma.

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