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Received July 30, 2018; Accepted December 8, 2018; Published December 16, 2018
Abstract. In 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.
How to Cite this Article:
Ishak Altun, Gonca Durmaz, Murat Olgun, P-contractive mappings on metric spaces, Journal of Nonlinear Functional Analysis, Vol. 2018 (2018), Article ID 43, pp. 1-7.