Partial Extended b-Metric Space and Some Fixed Point Theorems

Muhamad Abdillah Ahen, Ivan Hadinata, Ariqah Rif'at Rafilah Sapsuha

Abstract


Dalam makalah ini, kami memperkenalkan konsep ruang b-metrik diperluas parsial (PEBMS) sebagai penyatuan dan generalisasi ruang b-metrik diperluas dan ruang b-metrik parsial. Struktur baru ini menggabungkan fungsi kontrol yang bergantung pada titik bersama dengan kemungkinan jarak diri bukan nol, memberikan kerangka kerja yang lebih fleksibel untuk studi ruang metrik tergeneralisasi. Kami menetapkan beberapa sifat fundamental PEBMS, termasuk konvergensi dan barisan Cauchy. Dengan memperkenalkan gagasan barisan Cauchy, kami memperluas berbagai hasil dari ruang b-metrik diperluas ke pengaturan PEBMS. Secara khusus, kami membuktikan teorema titik tetap untuk pemetaan kontraktif dan menunjukkan keberadaan dan keunikan titik tetap di bawah kondisi yang sesuai. Lebih lanjut, kami menunjukkan bahwa setiap ruang b-metrik diperluas dapat dipandang sebagai kasus khusus dari PEBMS. Sebagai aplikasi, kami mempelajari stabilitas sistem dinamis diskrit dalam kerangka kerja ini. Hasil yang disajikan di sini menggeneralisasi dan memperkaya teori yang ada dalam ruang tipe metrik dan membuka arah baru untuk penelitian lebih lanjut.

Keywords


fixed point; metric space; contraction mapping

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References


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DOI: https://doi.org/10.18860/cauchy.v11i2.42921

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