Fs−contractive mappings in controlled metric type spaces
Fs−contractive mappings in controlled metric type spaces
We investigate in this manuscript, we study a new type of mappings so called F_s −contractive, in additionto we establish some fixed point results related to F_s −contractive type mappings in controlled type metricspaces. Also, examples are provided to illustrate our results.
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- [1] S. Banach, Sur les opérations dans les ensembles abstraits et leur applications aux équations intégrales, Fund Math. 3,
133-181 (1922).
- [2] J. Jachymski, I. Jówik, On Kirk's asymptotic contractions. J Math Anal Appl. 300, 147-159 (2004). doi:10.1016/j.
jmaa.2004.06.037.
- [3] T. Suzuki, Fixed-point theorem for asymptotic contractions of Meir-Keeler type in complete metric spaces, Non-linear
Anal. 64, 971-978 (2006).
- [4] N. Mlaiki, H. Aydi, N. Souayah and T. Abdeljawad, Controlled metric type spaces and the related contraction principle,
Mathematics, 6, 194, 2018.
- [5] A. Meir, E. Keeler, A theorem on contraction mappings. J Math Anal Appl. 28, 326-329 (1969). doi:10.1016/0022-247X
(69)90031-6.
- [6] T. Abdeljawad, Fixed points for generalized weakly contractive mappings in partial metric spaces. Math Comput Mod-
elling. 54, 2923-2927 (2011). doi:10.1016/j.mcm.2011.07.013.
- [7] Choudhury, Binayak, S, Konar, P, Rhoades, BE, Metiya, N: Fixed point theorems for generalized weakly contractive
mappings. Nonlinear Anal. 74, 2116-2126 (2011). doi:10.1016/j.na.2010.11.017.
- [8] D. Wardowski, Fixed points of a new type of contractive mappings in complete metric spaces. Fixed Point Theory Appl.
2012, 94 (2012) https://doi.org/10.1186/1687-1812-2012-94.
- [9] A. Lukács, S. Kajántó, Fixed point theorems for various types of F-contractions in complete b-metric spaces. Fixed Point
Theory 19(1), 321-334 (2018). https://doi.org/10.24193/fpt-ro.2018.1.25.
[10] S. Cobzas, Fixed points and completeness in metric and in generalized metric spaces (2016). arXiv:1508.05173v4 [math.FA]
[11] T.K. Hu, On a fixed-point theorem for metric spaces. Am. Math. Mon. 74, 436-437 (1967).
- [12] H. Garai, T. Senapati, L.K. Dey, A study on Kannan type contractive mappings (2017). arXiv:1707.06383v1 [math.FA].
- [13] F.E. Browder, W.V. Petryshyn, The solution by iteration of non-linear functional equations in Banach spaces. Bull. Am.
Math. Soc. 72, 571-575 (1966).
- [14] J.B. Baillon, R.E. Bruck, S. Reich, On the asymptotic behaviour of non-expansive mappings and semi-groups in Banach
spaces. Houst. J. Math. 4, 1-9 (1978).
- [15] R.E. Bruck, S. Reich, Non-expansive projections and resolvents of accretive operators in Banach spaces. Houst. J. Math.
3, 459-470 (1977).
- [16] J. Górnicki, Fixed point theorems for F-expanding mappings. Fixed Point Theory Appl. 2017, 9 (2017).
https://doi.org/10.1186/s13663-017-0602-3.
- [17] T. Abdeljawad, N. Mlaiki, H. Aydi, and N. Souayah, Double Controlled Metric Type Spaces and Some Fixed Point
Results, Mathematics 2018, 6, 320; doi:10.3390/math6120320
- [18] E. Karapinar, S. Czerwik, H. Aydi, (α,ψ)-Meir-Keeler contraction mappings in generalized b-metric spaces, Journal of
Function spaces, Volume 2018 (2018), Article ID 3264620, 4 pages.
- [19] H. Afshari, H. Aydi, E. Karapinar, On generalized α − ψ-Geraghty contractions on b-metric spaces, Georgian Math. J.
27 (2020), 9-21
- [20] E. Karapinar, A. Petrusel, and G.Petrusel, On admissible hybrid Geraghty contractions, Carpathian J. Math. 36 (2020),
No. 3, 433 - 442.
- [21] H. Aydi, M. F. Bota, E. Karapinar, S. Mitrovic, A fixed point theorem for set-valued quasi-contractions in b-metric spaces,
Fixed Point Theory Appl. 2012, 2012 :88.
- [22] H. Aydi, M.F. Bota, E. Karapinar, S. Moradi, A common fixed point for weak phi-contractions on b-metric spaces, Fixed
Point Theory, 13 (2) (2012), 337-346.
- [23] M.A. Alghamdi, S. Gulyaz-Ozyurt and E. Karapinar, A Note on Extended Z−Contraction, Mathematics, Volume 8 Issue
2 Article Number 195 (2020).