Perumuman Teorema Titik Tetap Pada Ruang Metrik Parsial

Nissa Fiska; Ahmad Hadra Zuhri; Rahma Zuhra; Dara Irsalina; Muhammad Rizqi Musa

doi:10.24843/JMAT.2026.v16.i01.p195

Penulis

Nissa Fiska Universitas Syiah Kuala
Ahmad Hadra Zuhri Universitas Syiah Kuala
Rahma Zuhra Universitas Syiah Kuala
Dara Irsalina Universitas Syiah Kuala
Muhammad Rizqi Musa Universitas Syiah Kuala

DOI:

https://doi.org/10.24843/JMAT.2026.v16.i01.p195

Kata Kunci:

Kondisi Kontraktif, Ruang Metrik Parsial, Teorema Irisan Cantor, Titik Tetap

Abstrak

Teori titik tetap memiliki peran yang sangat penting dalam analisis nonlinier, khususnya dalam menjamin keberadaan dan keunikan solusi dari berbagai permasalahan matematika, seperti persamaan diferensial, optimisasi, dan model-model ekuilibrium. Penelitian ini bertujuan untuk memperluas serta menyempurnakan hasil yang telah diperoleh oleh Gangopadhyay et al. terkait keunikan titik tetap pada ruang metrik parsial. Dengan mengadopsi pendekatan serupa, Teorema Irisan Cantor, studi ini secara sistematis mengeksplorasi keberadaan titik tetap untuk pemetaan yang memenuhi kondisi kontraktif yang telah digeneralisasi, sehingga memperluas cakupan dari teorema titik tetap klasik. Secara khusus, penelitian ini menganalisis kondisi kontraksi tipe Banach, Kannan, dan Chatterjea dalam kerangka ruang metrik parsial. Hasil utama menunjukkan bahwa pemetaan yang memenuhi kondisi kontraktif sebagaimana dirumuskan dalam Teorema 3.1 memiliki titik tetap tunggal. Temuan ini memperluas cakupan penerapan terhadap kelas pemetaan yang lebih luas dalam ruang metrik parsial, termasuk pemetaan transenden, self-adjust contractions, serta operator multivalued.

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