Some fixed point theorems for single valued strongly contractive mappings in partially ordered ultrametric and non-Archimedean normed spaces

Authors: HAMID MAMGHADERI, HASHEM PARVANEH MASIHA, MERAJ HOSSEINI

Abstract: 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.

Keywords: Fixed point, spherically complete ultrametric space, non-Archimedean normed space, strongly contractive mapping, partially ordered set

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