TThe work of non-Newtonian calculus was begun in 1972. This provides a different area to the classical one. Non-Newtonian metric concept defined 2002 by Basar and Cakmak. Then Binbaşıoğlu et al. had given spaces 2016. Also, they started fixed-point theory defining some topological properties spaces. In this work, we give theorems results for self-mappings satisfying certain conditions