TY - JOUR T1 - Fs−contractive mappings in controlled metric type spaces AU - Rizk, Doaa AU - Abuloha, Muhib AU - Abodayeh, Kamaleldin AU - Mukheimer, Aiman AU - Souayah, Nizar PY - 2021 DA - September DO - 10.53006/rna.928319 JF - Results in Nonlinear Analysis JO - RNA PB - Erdal KARAPINAR WT - DergiPark SN - 2636-7556 SP - 149 EP - 158 VL - 4 IS - 3 LA - en AB - 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. KW - controlled metric space KW - weakly contractive mapping KW - fixed point CR - [1] S. Banach, Sur les opérations dans les ensembles abstraits et leur applications aux équations intégrales, Fund Math. 3, 133-181 (1922). CR - [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. CR - [3] T. Suzuki, Fixed-point theorem for asymptotic contractions of Meir-Keeler type in complete metric spaces, Non-linear Anal. 64, 971-978 (2006). CR - [4] N. Mlaiki, H. Aydi, N. Souayah and T. Abdeljawad, Controlled metric type spaces and the related contraction principle, Mathematics, 6, 194, 2018. CR - [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. CR - [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. CR - [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. CR - [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. CR - [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). CR - [12] H. Garai, T. Senapati, L.K. Dey, A study on Kannan type contractive mappings (2017). arXiv:1707.06383v1 [math.FA]. CR - [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). CR - [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). CR - [15] R.E. Bruck, S. Reich, Non-expansive projections and resolvents of accretive operators in Banach spaces. Houst. J. Math. 3, 459-470 (1977). CR - [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. CR - [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 CR - [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. CR - [19] H. Afshari, H. Aydi, E. Karapinar, On generalized α − ψ-Geraghty contractions on b-metric spaces, Georgian Math. J. 27 (2020), 9-21 CR - [20] E. Karapinar, A. Petrusel, and G.Petrusel, On admissible hybrid Geraghty contractions, Carpathian J. Math. 36 (2020), No. 3, 433 - 442. CR - [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. CR - [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. CR - [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). UR - https://doi.org/10.53006/rna.928319 L1 - https://dergipark.org.tr/en/download/article-file/1734766 ER -