Geodesic
Some new fixed point results in $\mathrm{b}$-metric space with rational generalized contractive condition
Žurnal Sibirskogo federalʹnogo universiteta. Matematika i fizika, Tome 16 (2023) no. 4, pp. 506-518.

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In this paper, we improve and generalize several results in fixed point theory to the $\mathrm{b}$-metric space. Where we confirm the existence of the fixed point for self mapping $T$ satisfying some rational contractive conditions. Over-more, we establish the uniqueness of the fixed point in some cases and give dynamic information linking the fixed points between them in the other cases. Some illustrative examples are furnished, which demonstrate the validity of the hypotheses.
Keywords: metric space, $\mathrm{b}$-metric space, Picard sequence, Fixed point, Rational contraction mapping. 
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Besma Laouadi; Taki Eddine Oussaeif; Leila Benaoua; Liliana Guran; Stojan Radenović. Some new fixed point results in $\mathrm{b}$-metric space with rational generalized contractive condition. Žurnal Sibirskogo federalʹnogo universiteta. Matematika i fizika, Tome 16 (2023) no. 4, pp. 506-518. http://geodesic.mathdoc.fr/item/JSFU_2023_16_4_a8/

[1] S.Aleksić, H.Huang, Z.D.Mitrović, S.Radenović, “Remarks on some fixed point results in b-metric spaces”, Journal of Fixed Point Theory and Applications, 20:4 (2018), 1–17 | DOI | MR

[2] S.Aleksić, Z.Mitrovic, S.Radenovic, “Picard sequences in b-metric spaces”, Fixed Point Theory, 21 (2020) | DOI | MR | Zbl

[3] A.Aghajani, M.Abbas, J.R.Roshan, “Common fixed point of generalized weak contractive mappings in partially ordered b-metric spaces”, Mathematica Slovaca, 64:4 (2014), 941–960 | DOI | MR | Zbl

[4] A.C.Aouine, A.Aliouche, “Fixed point theorems Of Kannan type With an application to control theory”, Applied Mathematics E-Notes, 21 (2021), 238–249 | MR | Zbl

[5] I.A.Bakhtin, “The contraction mapping principle in quasi metric spaces”, Funct. Anal. Unianowsk Gos. Ped. Inst., 30 (1989), 26–37 | MR | Zbl

[6] S.Banach, “On operations in abstract sets and their applications to integral equations”, Fund. Math., 3:1 (1922), 133–181 | DOI | MR

[7] V.Berinde, M.Pacurar, “The early developments in fixed point theory on b-metric spaces”, Carpathian Journal of Mathematics, 38:3 (2022), 523–538 | DOI | MR

[8] N.Bourbaki, General Topology, Herman, Paris, 1974 | MR

[9] S.Czerwik, “Contraction mappings in b-metric spaces”, Acta mathematica et informatica universitatis ostraviensis, 1:1 (1993), 5–11 | MR | Zbl

[10] P.Debnath, N.Konwar, S.Radenovic, Metric fixed point theory, Applications in science, engineering and behavioural sciences, 2021 | MR | Zbl

[11] H.S.Ding, M.Imdad, S.Radenović, J.Vujaković, “On some fixed point results in b-metric, rectangular and b-rectangular metric spaces”, Arab Journal of Mathematical Sciences, 22:2 (2016), 151–164 | DOI | MR | Zbl

[12] T.M.Dośenović, M.V.Pavlović, S.N.Radenović, “Contractive conditions in b-metric spaces”, Military Technical Gazette Courier, 65:4 (2017), 851–865 | MR

[13] N.Goswami, N.Haokip, V. N.Mishra, “F-contractive type mappings in b-metric spaces and some related fixed point results”, Fixed Point Theory and Applications, 2019, no. 1, 1–17 | DOI | MR

[14] H.Huang, G.Deng, S.Radenović, “Fixed point theorems in b-metric spaces with applications to differential equations”, Journal of Fixed Point Theory and Applications, 20:1 (2018), 1–24 | DOI | MR | Zbl

[15] N.Hussain, D.Dorić, Z.Kadelburg, S.Radenović, “Suzuki-type fixed point results in metric type spaces”, Fixed point theory and applications, 2012:1 (2012), 12 pp. | MR

[16] N.Hussain, Z.D.Mitrović, S.Radenović, “A common fixed point theorem of Fisher in b-metric spaces”, RACSAM, 113 (2019), 949–956 | DOI | MR

[17] Z.Kadelburg, S.Radenović, “Notes on Some Recent Papers Concerning F-Contractions in b-Metric Spaces”, Constructive Mathematical Analysis, 1:2 (2018), 108–112 | DOI | MR | Zbl

[18] Z.Kadelburg, S.Radenovic, “Pata-type common fixed point results in b-metric and b-rectangular metric spaces”, J. Nonlinear Sci. Appl., 8:6 (2015), 944–954 | DOI | MR | Zbl

[19] T.Kamran, M.Samreen, Q. UL Ain, “A Generalization of b-Metric Space and Some Fixed Point Theorems”, Mathematics, 5:2 (2017), 19 | DOI | MR | Zbl

[20] F.Khojasteh, M.Abbas, S.Costache, “Two new types of fixed point theorems in complete metric spaces”, Abstract and Applied Analysis, 2014 (2014), 325840 | DOI | MR | Zbl

[21] M.Kir, H.Kiziltune, “On some well known fixed point theorems in b-metric spaces”, Turkish journal of analysis and number theory, 1:1 (2013), 13–16 | DOI | MR

[22] A.Lukacs, S.Kajanto, “Fixed point theorems for various types of Fcontractions in complete b-metric spaces”, Fixed Point Theory, 19 (2018), 321–334 | DOI | MR | Zbl

[23] Z.D.Mitrovic, S.Radenovic, F.Vetro, J.Vujakovic, “Some remarks on TAC-contractive mappings in b-metric spaces”, Mat. Vesnik, 70:2 (2018), 167–175 | MR | Zbl

[24] N.Mlaiki, N.Dedovic, H.Aydi, M.Gardasević-Filipović, B.Bin-Mohsin, S.Radenović, “Some new observations on Geraghty and Cirić type results in b-metric spaces”, Mathematics, 7:7 (2019), 643 | DOI

[25] V.Ozturk, S.Radenović, “Some remarks on b-(EA)-property in bmetric spaces”, SpringerPlus, 5:544 (2016), 1–10 | DOI

[26] S.Radenović, T.Dośenović, T.A.Lampert, Z.Golubovíć, “A note on some recent fixed point results for cyclic contractions in b-metric spaces and an application to integral equations”, Applied Mathematics and Computation, 273 (2016), 155–164 | DOI | MR | Zbl

[27] J.R.Roshan, V.Parvaneh, S.Radenović, M.Rajović, “Some coincidence point results for generalized $(\psi, \phi)$-weakly contractions in ordered b-metric spaces”, Fixed Point Theory and Applications, 2015 (2015), 68, 21 pp. | DOI | MR | Zbl