Suzuki type P-contractive mappings

Abstract

We introduce Suzuki type P-contractive mappings by taking into account the concepts of contractive, P-contractive, and Suzuki type contractive mappings. Then, for such mappings on compact metric spaces, we present a fixed point theorem that is more general than the well-known Edelstein fixed point theorem.

Keywords

• Fixed point
• contractive mapping
• compact metric space

References

1. R.P. Agarwal, D. O’Regan, D.R. Sahu, Fixed Point Theory for Lipschitzian-type Mappings and Applications, Springer, New York, 2009.
2. I. Altun, G. Durmaz, M. Olgun, P-contractive mappings on metric spaces, Journal of Nonlinear Functional Analysis, 2018 (2018), Article ID 43, pp. 1-7.
3. I. Altun, H.A. Hancer, Almost Piacrd operators, AIP Conference Proceedings 2183, 060003 (2019); https://doi.org/10.1063/1.5136158
4. M. Edelstein, On fixed and periodic points under contractive mappings, J. London Math. Soc., 37 (1962) 74-79.
5. T. Suzuki, A new type of fixed point theorem in metric spaces, Nonlinear Anal., 71 (2009), 5313-5317.