Fixed Point Theorem on Contractive Mapping in Standard 2-Normed Spaces
DOI:
https://doi.org/10.20956/j.v18i1.14394Keywords:
mathematic, functional analysis, fixed point theorem, 2-normed spacesAbstract
This paper discussed about the proof of the fixed point theorem on the standard 2-normed spaces by using completeness. The completeness of the standard 2-normed spaces is shown by defining a new norm. Two linear independent vectors on standard 2-normed spaces are used to define the new norm, namely which has been shown to be equivalent to standard norm.Downloads
References
Anton, H., Rorres, C., 2005. Elementary Linear Algebra. Newyork: John Wiley & Sons Inc.
Conway, J.,1997. A Course in Functional Analysis. Newyork: Springer-Verlag.
Gӓhler, S.,1964. Lineare 2-Nomierte Rӓume. Math Nachr, Vol. 28, pp. 1-43.
Gunawan, H., 2001. The Space of p-Summable Sequences and Its Natural n-Norm. Bull Australia Math Soc, Vol. 64, pp. 137-147.
Gunawan, H., Mashadi., 2001. On Finite Dimensional 2-Normed Spaces. Soochow Journal of Mathematics, vOL. 27, pp. 321-329.
Haase, M., 2010. Functional Analysis: An Elementary Introduction. Rhode Island : American Mathematical Society Providance.
Handayani, A., 2013. Skripsi: Barisan pada Ruang Norm-2. Jurusan Matematika Fakultas Sains dan Teknologi UIN Malang.
Harikrishnan, K., Ravindran, T., 2011. Some Properties of Accretive Operators in Linier 2-Normed Space. Int. Mathematical Forum, Vol. 3, No. 59, pp. 2941-2947.
Imrona, M., 2002. Aljabar Linier Elementer. Bandung: Sekolah Tinggi Teknologi Telkom.
Kreyszig, E. (1978). Introductory Functional Analysis With Application. Newyork: John Wiley dan Sons Inc.
Lidiyani, Y., Shiddiq, M. (2017). Teorema Titik Tetap untuk Pemetaan Kontraksi-F yang Diperumum pada Ruang Seperti-Metrik-b. Jurnal Matematika Murni dan Terapan “Epsilon”, 11, 36-46.
Manuhutu, J., Lesnussa, A., Batkunde, H. (2014). Ruang Norm-2 dan Ruang Hasil Kali Dalam-2. Jurnal Matematika Integratif, Vol. 10, pp. 139-145.
Nur, M., 2011. Tesis: Teorema Titik Tetap di Ruang Norm-n Standar. Institut Teknologi Bandung.
Nur, M., 2012. Teorema Titik Tetap di Ruang Norm-2 Standar. Jurnal Matematika, Statistika dan Komputasi, pp. 1-6.
Resmawan., 2019. Materi Kuliah Aljabar Linear. Math UNG, Universitas Negeri Gorontalo.
Rudin, W., 1991. Functional Analysis. Singapore: McGraw-Hill.
Rumlawang, F. Y., 2020. Fixed Point Theorem in 2-Normed Spaces. Tensor Pure and Applied Mathematic’s Journal, Vol. 1, pp. 41-46.
Rynne, B.P., Youngson, M. A., 2000. Linier Functional Analysis. London: Springer-Verlag.
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This work is licensed under a Creative Commons Attribution 4.0 International License.
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