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

Malahayati Malahayati


DOI: https://doi.org/10.14710/jfma.v1i1.5

Abstract


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.

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References


. A.E. Bashirov, E.M.Kurpnar and A. Ozyapc. Multiplicative calculus and its Applications, J.Math. Analysis.App., 337 (2008) hal 36-48.

. Bartle, R.G and Sherbert, D.R. 2010.

Introduction to Real Analysis. Fourt Edition. New York: John Wiley & Sons. Inc.

. M. Edelstein, On fixed and periodic points under contractive mappings, J. London Math. Soc.(37), 74–79 (1962).

. M. Ozavsar` and A.C. Cevikel, Fixed Point of Multiplicative contraction mapping on multiplicative metric space. J. Arxiv: 1205.5131v1 [math.GM] 23 May 2012.

. R. P. Agarwal, M. A. El-Gebily, and D. ORegan, Generalized contractions in partially ordered metric spaces, Appl. Anal. 87,109–116 (2008)

.Shirali, Satish and Vasudeva, Harkrishan L. 2006. Metric Spaces. London: Springer-Verlag.

. Sarwar, M. and Badshah-e-Rome, Some Unique Fixed Point Theorems in Multiplicative Metric Space, J. Arxiv:1410.3384v2 [math.GM] 29 Desember 2014.

. Z. Mustafa, Z, B. Sims, A new approach to a generalized metric spaces. J. Nonlinear Convex Anal. 7(2) (2006), 289297. MR2254125 (2007f:54049)


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