%A NIM.: 18106010013 Mesaliani Negara
%O Pembimbing: Malahayati, S.Si., M.Sc dan Dr. Muhammad Wakhid Musthofa, S.Si., M.Si
%T EKSISTENSI TITIK TETAP PADA PEMETAAN KONTRAKSI ENRICHED DI RUANG METRIK KONVEKS
%X 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.
%K Titik Tetap, Ruang Metrik Konveks, Kontraksi Enriched
%D 2022
%I UIN SUNAN KALIJAGA YOGYAKARTA
%L digilib54409