P-CONTRACTIVE MAPPINGS ON METRIC SPACES

Altun, Ishak/0000-0002-7967-0554WOS: 000454873800004In the present paper, we introduce a new concept of P-contractive mappings on metric spaces. We prove that every ordinary contractive mapping is also P-contractive but the converse may not be true in general. We provide an example to illustrate this fact and also provide some examples to show that nonexpensive mappings and P-contractive mappings are independent on metric spaces. Finally, we present that every continuous P-contractive mapping on compact metric spaces has a unique fixed point. This result includes the famous Edelstein fixed point theorem