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.

DOI

10.3906/mat-1412-3

Keywords

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

First Page

9

Last Page

14

Recommended Citation

MAMGHADERI, H, MASIHA, H. P, & HOSSEINI, M (2017). Some fixed point theorems for single valued strongly contractive mappings in partially ordered ultrametric and non-Archimedean normed spaces. Turkish Journal of Mathematics 41 (1): 9-14. https://doi.org/10.3906/mat-1412-3