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Spherical Functions on Fuzzy Lie Group
Department of Mathematics, University of Ibadan, Ibadan, Nigeria
Department of Mathematics, University of Ibadan, Ibadan, Nigeria
- 1 Department of Mathematics, University of Ibadan, Ibadan, Nigeria
- 2 Department of Mathematics, University of Ibadan, Ibadan, Nigeria
Advances in Pure Mathematics·Volume 14 (2024)·Pages 185–195·Published 3 April 2024·DOI10.4236/apm.2024.144010
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Abstract
Let <i>G</i> be a locally compact Lie group and <img src="https://html.scirp.org//file/5302366-rId13.svg?20240402112528" /> its Lie algebra. We consider a fuzzy analogue of <i>G,</i> denoted by <img src="https://html.scirp.org//file/5302366-rId15.svg?20240402112528" /> called a fuzzy Lie group. Spherical functions on <img src="https://html.scirp.org//file/5302366-rId17.svg?20240402112528" /> are constructed and a version of the existence result of the Helgason-spherical function on <i>G</i> is then established on <img src="https://html.scirp.org//file/5302366-rId19.svg?20240402112528" />.
KeywordsFuzzy Spherical FunctionFuzzy Lie GroupFuzzy Manifolds
- Zadeh, L.A. (1965) Fuzzy Sets. Fuzzy Information and Control , 8, 177-200. https://doi.org/10.1016/S0019-9958(65)90241-X
- Kastaras, A.K. (1981) Topological Linear Spaces I. Fuzzy Sets and Systems , 6, 85-95. https://doi.org/10.1016/0165-0114(81)90082-8
- Kastaras, A.K. (1984) Topological Linear Spaces II. Fuzzy Sets and Systems , 12, 143-154. https://doi.org/10.1016/0165-0114(84)90034-4
- Kastaras, A.K. and Liu, D.B. (1977) Fuzzy Vector Spaces and Fuzzy Topological Vector Spaces. Journal of Mathematical Analysis and Applications , 58, 135-146. https://doi.org/10.1016/0022-247X(77)90233-5
- Kubiak, T. (1985) On Fuzzy Topologies. Ph. D. Thesis, Adam Mickiewicz, Poznan.
- Sostak, A.P. (1985) On a Fuzzy Topological Structure. Proceedings of the 13 th Wi n ter School on Abstract Analysis , Circolo Matematico di Palermo, 89-103.
- Egwe, M.E. and Oyewo, R.A. (2021) A Fixed Point Theorem on Fuzzy Locally Convex Spaces. Annals of Fuzzy Mathematics and Informatics , 22, 17-24. https://doi.org/10.20944/preprints202206.0311.v1
- Chakraborty, M. and Ahsanullah, T. (1992) Fuzzy Topology on Fuzzy Sets and Tolerance Topology. Fuzzy Sets and Systems , 45, 103-108. https://doi.org/10.1016/0165-0114(92)90096-M
- Akram, M. (2018) Fuzzy Lie Algebras. Springer Verlag, Berlin. https://doi.org/10.1007/978-981-13-3221-0
- Nadjafikhah, M. and Bakhshandeh-Chamazkoti, R. (2009) Fuzzy Lie Groups. M a thematical Sciences , arXiv: 0908.0254. https://arxiv.org/abs/0908.0254v1
- Godement, R. (1952) A Theory of Spherical Functions I. Trans. Transactions of the American Mathematical Society , 73, 496-556. https://doi.org/10.1090/S0002-9947-1952-0052444-2
- Chandra, H. (1958) Spherical Functions on a Semisimple Lie Group, I. American Mathematical Society , 80, 241-310. https://doi.org/10.2307/2372786
- Egwe, M.E. (2020) On Fixed Point Theorem in Non-Archimedean Fuzzy Normed Spaces. International Journal of Analysis and Applications , 18, 99-103.
- Yeol, J.C., Rassias, T.M. and Saadati, R. (2018) Fuzzy Operator Theory in Mathematical Analysis. Springer Verlag, Berlin.
- Helgason, S. (1984) Groups and Geometric Analysis: Radon Transforms, Invariant Differential Operators and Spherical Functions: Volume 1. Academic Press, Cambridge.