Subsemigroup of Signed Contraction Mapping of Full Transformation Semigroup
I. A. Ogunleke, K. Rauf, Morufu Mogbolagade Mogbonju · Asian Journal of Current Research · 2025
The full transformation semigroup, Tn on the set Xn = {1,2,3, ... } is the set of all maps \(\alpha\): Xn \(\to\) Xn, under the operation of composition of mapping. The signed contraction mappings of full transformation and its subsemigroup \(\alpha\) \(\in\) SCTn is a contraction for all if |i\(\alpha\)|-|i\(\alpha\)| = |i|-|j|and is defined on the set \(\alpha\): Xn \(\to\) Z* where Z* = Z/{0} and Z* = {-n ..., -3, -2,1,2,3 ..., n}. The cardinality of signed order preserving of full contraction mapping, SOCTn,order decreasing signed full contraction mapping, and both order preserving and order decreasing signed full contraction mapping, SOCTn, are obtained. The results are tabulated based on the number of positive and negative elements in the domain of \(\alpha\) [Dom(\(\alpha\))}.