Existence and Uniqueness of Fixed Point for Cyclic Mappings in Quasi-αb-Metric Spaces
Abstract
The fixed point theory remains the most important and preferred topic studied in mathematical analysis. This study discusses sufficient conditions to prove a unique fixed point in quasi-αb-metric spaces with cyclic mapping. The analysis starts by showing fulfillment of the cyclic Banach contraction and proving the Cauchy sequence as a condition for proving a unique fixed point in quasi-αb-metric spaces with cyclic mapping. Furthermore, it's shown that the cyclic mappings, T have a unique fixed point in quasi-αb-metric spaces. Finally, an example is given to strengthen the proof of the theorems that have been done.
Keywords: fixed point theory; Quasi -Metric spaces; Cyclic Banach Contraction; Cauchy sequence.
Abstrak
Teori titik tetap termasuk salah satu topik penting dan menarik untuk diteliti pada bidang analisis. Pada penelitian ini, dibahas tentang syarat cukup dalam membuktikan bahwa terdapat titik tetap tunggal dalam ruang quasi- b-metrik pada pemetaan siklik. Analisis diawali dengan menunjukkan pemenuhan kondisi kontraksi Banach siklik dan pembuktian barisan Cauchy sebagai syarat pembuktian bahwa terdapat titik tetap tunggal pada pemetaan siklik dalam ruang quasi- b-metrik. Selanjutnya ditunjukkan bahwa pemetaan siklik memiliki titik tetap tunggal dalam ruang quasi b-metrik. Terakhir, diberikan contoh untuk memperkuat pembuktian teorema yang telah dilakukan.
Kata Kunci: teori titik tetap; ruang Quasi -Metrik; Kontraksi Banach Siklik; barisan Cauchy.
Keywords
References
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DOI: 10.15408/inprime.v4i1.24462
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