KONSEP DASAR DAN SIFAT LENGKAP RUANG METRIK-bv

Diaz Mayangkara, NIM.: 17106010028 (2022) KONSEP DASAR DAN SIFAT LENGKAP RUANG METRIK-bv. Skripsi thesis, UIN SUNAN KALIJAGA YOGYAKARTA.

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Abstract

The metric space is one of most important concepts in the realm of functional analysis, it is said to be important because metric space is widely used in other mathematical theories, one of which is a fixed point. Metric space experienced many developments including b-metric space and v-metric space. Both metric space were developed again into bv-metric space. The bv-metric space was first introduced by Mitrovic and Radenovic in 2017. The bv-metric space is a non-empty set in which it is completed by a mapping and satisfies three axioms namly singularity, symmetry, inequality of the bv. The bv-metric space is generalized metric space or it can be said that the metric space is a special case of the bv-mertic space. The relationship between metric space and bv-metric space will be explained in this discussed, including the concept of convergent sequence and Cauchy sequence in bv-metric space. The concept of such a sequence is used in the process of proving the complete nature of the bv-metric space, so that the complete nature of the bv-metric space is proved.

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