Let $ (X,d,\preceq) $ be a partially ordered ultrametric space and $ f:X\to X $ a single valued mapping. We obtain sufficient conditions for the existence of a fixed point for the strongly contractive mapping $ f $. We also investigate the existence of a fixed point for strongly contractive mappings defined on partially ordered non-Archimedean normed spaces under the same conditions. Finally, we give some examples to discuss the assumptions of the theorems.
MAMGHADERI, HAMID; MASIHA, HASHEM PARVANEH; and HOSSEINI, MERAJ
"Some fixed point theorems for single valued strongly contractive mappings in partially ordered ultrametric and non-Archimedean normed spaces,"
Turkish Journal of Mathematics: Vol. 41:
1, Article 2.
Available at: https://journals.tubitak.gov.tr/math/vol41/iss1/2