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.
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.
Downloads
Published
Issue
Section
License
Copyright (c) 2021 Author and publisher
This work is licensed under a Creative Commons Attribution 4.0 International License.
This work is licensed under a Creative Commons Attribution 4.0 International License.
Jurnal Matematika, Statistika dan Komputasi is an Open Access journal, all articles are distributed under the terms of the Creative Commons Attribution License, allowing third parties to copy and redistribute the material in any medium or format, transform, and build upon the material, provided the original work is properly cited and states its license. This license allows authors and readers to use all articles, data sets, graphics and appendices in data mining applications, search engines, web sites, blogs and other platforms by providing appropriate reference.
