A remark on Secelean–Wardowski’s fixed point theorems
Tóm tắt
In this paper we give a simple proof of three fixed point theorems of Secelean and Wardowski by using the fixed point result of Jachymski et al. Our result is established with weaker assumptions than the three theorems. Furthermore, the recent result of Secelean et al. in the setting of a complete metric space can be also deduced by our theorem.
Tài liệu tham khảo
Jachymski, J., Matkowski, J., Swiatkowski, T.: Nonlinear contractions on semimetric spaces. J. Appl. Anal. 1(2), 125–134 (1995)
Secelean, N.A.: Iterated function systems consisting of F-contractions. Fixed Point Theory Appl. 2013, Article ID 277 (2013)
Secelean, N.A., Mathew, S., Wardowski, D.: New fixed point results in quasi-metric spaces and applications in fractals theory. Adv. Differ. Equ. 2019, Article ID 177 (2019). https://doi.org/10.1186/s13662-019-2119-z
Secelean, N.A., Wardowski, D.: ψF-contractions: not necessarily nonexpansive Picard operators. Results Math. 70, 415–431 (2016)
Wardowski, D.: Fixed points of a new type of contractive mappings in complete metric spaces. Fixed Point Theory Appl. 2012, Article ID 94 (2012). https://doi.org/10.1186/1687-1812-2012-94