EKSISTENSI TITIK TETAP PADA PEMETAAN KONTRAKSI ENRICHED DI RUANG METRIK KONVEKS

Mesaliani Negara, NIM.: 18106010013 (2022) EKSISTENSI TITIK TETAP PADA PEMETAAN KONTRAKSI ENRICHED DI RUANG METRIK KONVEKS. Skripsi thesis, UIN SUNAN KALIJAGA YOGYAKARTA.

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Abstract

Convex metric spaces is one of the extensions of the usual metric concept. The convex metric space introduced by Takahashi in 1970. The convex metrik space is non-empty set X with metric d that have a convex structure. Then in 2021 Vasile and Berinde introduced the mapping of Enriched Contractions in the metric space which is an extension of the Banach contraction mapping principle in the metric space. This study discusses the convex metric space, mapping of enriched contractions and fixed point theorem of enriched contraction mappings in convex metric space. The proof of the fixed point theorem has the following steps. First, a Picard’s sequence is formed so from that sequence we get a Cauchy sequence that converges to a point. Furthermore, this point is one of the candidate fixed points in enriched contraction mapping. Then it is shown that the fixed point of the mapping has a unique fixed point. In this study, it was found that every enriched contraction mappings in convex metric space has a single point by forming a Picard sequence through mapping that defines convex structure in the convex metric space. In addition, it will given an example of the definition of convex metric space and the mapping of enriched contractions that has not been given by the previous author.

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