ANALISIS BEBERAPA TEOREMA KETUNGGALAN TITIK TETAP DI RUANG METRIK MULTIPLIKATIF (MULTIPLICATIVE METRIC SPACES)

This research was conducted to analyze several theorems about fixed point uniqueness on multiplicative metric space. Firstly, the proof of fixed point uniqueness theorem on complete multiplicative metric space is analyzed with involving multiplicative continuous functions. Then, several fixed point uniqueness theorems is analyzed without involving multiplicative continuous functions. The proof of fixed point uniqueness theorem on complete multiplicative metric space with involving multiplicative continuous functions can be done without requirement of contraction multiplicative mapping. If this mapping is satisfying a condition with involving multiplicative continuous functions then it was proven that it had the unique fixed point. Furthermore, the proof of fixed point uniqueness theorem on complete multiplicative metric space without involving multiplicative continuous functions can be done by requiring the mapping is contraction.

The Multiplicative Groups of Quasifields

Let (Q, +, ·) be a finite quasifield of dimension d over its kernel K = GF(q), where q = pk with p a prime and k ≧ 1. (See p. 18-22 and p. 74 of [7] or Section 5 of [9] for the definition of quasifield.) For the remainder of this article we will follow standard conventions and omit, whenever possible, the binary operations + and · in discussing a quasifield. For example, the notation Q will be used in place of the triple (Q, +, ·) and Q* will be used to represent the multiplicative loop (Q − {0}, ·).Let m be a non-zero element of the quasifield Q; the right multiplicative mapping ρm:Q → Q is defined by1