Fs−contractive mappings in controlled metric type spaces

Year 2021, , 149 - 158, 30.09.2021

Muhib Abuloha Doaa Rizk , Kamaleldin Abodayeh , Aiman Mukheimer Nizar Souayah

https://doi.org/10.53006/rna.928319

Cited By: 1

Abstract

We investigate in this manuscript, we study a new type of mappings so called F_s −contractive, in addition
to we establish some fixed point results related to F_s −contractive type mappings in controlled type metric
spaces. Also, examples are provided to illustrate our results.

Keywords

controlled metric space, weakly contractive mapping, fixed point

Supporting Institution

none

Project Number

none

Thanks

It is my pleasure to publish your journal

References

• [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).