Characterization of quasi idempotent in semigroups of full contraction mappings

Authors

  • A. D. Adeshola Department of Mathematics and Statistics, Kwara State University, Malete, P.M.B. 1530, Ilorin, Nigeria
  • S. O. Akande Department of Mathematics and Statistics, Kwara State University, Malete, P.M.B. 1530, Ilorin, Nigeria
  • R. G. Ibrahim Department of Mathematics and Statistics, Kwara State University, Malete, P.M.B. 1530, Ilorin, Nigeria
  • J. O. Lawal Department of Mathematics, Kwara State College of Education, Ilorin, Nigeria

Keywords:

Semigroup, Contraction mapping, Quasi-idempotent

Abstract

Let Tn be the semigroup of full transformation of a finite set and let Xn = {1, 2, · · · , n}. A transformation α : Domα ⊂ Xn →Im(α) ⊂ Xn is said to be full or total transformation if Domα = Xn. A transformation β ∈ CT n is said to be full contraction mapping if ∀ x, y ∈ Domα, |xα − yα| ≤ |x − y| ∀ x, y ∈ Domα. Let CT n be the semigroup of full contraction transformation and let QCT n be its quasi-idempotent of full contraction transformation of Xn. In this paper, we characterized quasi-idempotent elements into matching blocks, non-matching blocks and self matching blocks of CT n and later come up with a strong and useful theorem

Dimensions

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Published

2024-03-28

How to Cite

Characterization of quasi idempotent in semigroups of full contraction mappings. (2024). Proceedings of the Nigerian Society of Physical Sciences, 1(1), 88. https://doi.org/10.61298/pnspsc.2024.1.88

Issue

Volume 1, NSPS-KWASU Conference, Feb. 1- 4, 2024

Section

Articles
Copyright & Licensing

Copyright (c) 2024 A. D. Adeshola, S. O. Akande, R. G. Ibrahim, J. O. Lawal (Author)

Creative Commons License

This work is licensed under a Creative Commons Attribution 4.0 International License.

How to Cite

Characterization of quasi idempotent in semigroups of full contraction mappings. (2024). Proceedings of the Nigerian Society of Physical Sciences, 1(1), 88. https://doi.org/10.61298/pnspsc.2024.1.88