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Coupled fixed points of generalized rational type Z-contraction maps in b-metric spaces | ||
| International Journal of Nonlinear Analysis and Applications | ||
| مقاله 67، دوره 13، شماره 2، مهر 2022، صفحه 789-802 اصل مقاله (429.42 K) | ||
| نوع مقاله: Research Paper | ||
| شناسه دیجیتال (DOI): 10.22075/ijnaa.2020.20566.2172 | ||
| نویسندگان | ||
| Velisela Amarendra Babu1؛ Dasari Ratna Babu2؛ Nasina Siva Prasad* 3، 4 | ||
| 1Department of Mathematics, Acharya Nagarjuna University, Guntur - 522 510, India | ||
| 2Department of Mathematics, PSCMRCET, Vijayawada - 520 001, India | ||
| 3Department of Mathematics, Rayalaseema University, Kurnool - 518 007, India | ||
| 4Department of Mathematics, PBR VITS, Kavali- 524 201, India | ||
| تاریخ دریافت: 17 فروردین 1399، تاریخ بازنگری: 19 خرداد 1399، تاریخ پذیرش: 10 تیر 1399 | ||
| چکیده | ||
| In this paper, we introduce generalized rational type $\mathcal{Z}$-contraction maps for a single map $f:X\times X\to X$ where $X$ is a $b$-metric space and prove the existence and uniqueness of coupled fixed points. We extend it to a pair of maps by defining generalized rational type $\mathcal{Z}$-contraction pair of maps and prove the existence of common coupled fixed points in complete $b$-metric spaces. We provide examples in support of our results. | ||
| کلیدواژهها | ||
| coupled fixed points؛ $b$-metric space؛ generalized rational type $mathcal{Z}$-contraction maps | ||
| مراجع | ||
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[1] A. Aghajani, M. Abbas and J. R. Roshan, Common fixed point of generalized weak contractive mappings in partially ordered b-metric spaces, Math. Slovaca 64 (2014), no. 4, 941–960. [2] H. Aydi, M-F. Bota, E. Karapinar and S. Mitrovi¸c, A fixed point theorem for set-valued quasi contractions in b-metric spaces, Fixed Point Theory Appl. 88 (2012), 8 pages. [3] H. Aydi, M-F. Bota, E. Karapinar and S. Moradi, A common fixed point for weak ϕ-contractions on b-metric spaces, Fixed Point Theory 13 ( 2012), no. 2, 337–346. [4] G.V.R. Babu, T.M. Dula and P.S. Kumar, A common fixed point theorem in b-metric spaces via simulation function, J. Fixed Point Theory 12 (2018), 15 pages. [5] I.A. Bakhtin, The contraction mapping principle in almost metric spaces, Funct. Anal. Gos. Ped. Inst. Unianowsk 30 (1989), 26–37. [6] T.G. Bhaskar and V. Lakshmikantham, Fixed point theorems in partially ordered metric spaces and applications, Nonlinear Anal. 65 (2006), 1379–1393. [7] B. Bindu and N. Malhotra, Common coupled fixed point for generalized rational type contractions in b-metric spaces, J. Nonlinear Analy. Appl. 2018 (2018), no. 2, 201–211. [8] M. Boriceanu, Strict fixed point theorems for multivalued operators in b-metric spaces, Int. J. Mod. Math. 4 (2009), no. 3, 285–301. [9] M. Boriceanu, M.-F. Bota and A. Petrusel, Multivalued fractals in b-metric spaces, Cent. Eur. J. Math. 8 (2010), no. 2, 367-377. [10] N. Bourbaki, Topologie generale, Herman: Paris, France, 1974. [11] S. Czerwik, Contraction mappings in b-metric spaces, Acta Math. Inform. Univ. Ostraviensis 1 (1993), 5–11. [12] S. Czerwik, Nonlinear set-valued contraction mappings in b-metric spaces, Atti Sem. Mat. Fis. Univ. Modena 46 (1998), 263–276. [13] B.K. Dass and S. Gupta, An extension of Banach contraction principle through rational expressions, Indian J. Pure Appl. Math. 6 (1975), 1455–1458. [14] H. Huang, L. Paunovi¸c and S. Radenovi¸c, On some fixed point results for rational Geraghty contractive mappings in ordered b-metric spaces, J. Nonlinear Sci. Appl. 8 (2015), 800–807. [15] N. Hussain, V. Paraneh, J.R. Roshan and Z. Kadelburg, Fixed points of cycle weakly (ψ, φ, L, A, B)-contractive mappings in ordered b-metric spaces with applications, Fixed Point Theory Appl. 2013 (2013), 256, 18 pages. [16] N. Hussain, J.R. Roshan, V. Parvaneh and M. Abbas, Common fixed point results for weak contractive mappings in ordered b-dislocated metric spaces with applications, J. Inequal. Appl. 2013 (2013), 486, 21 pages. [17] F. Khojasteh, S. Shukla and S. Redenovic, A new approach to the study fixed point theorems via simulation functions, Filomat 29 (2015), no. 6, 1189–1194. [18] P. Kumam and W. Sintunavarat, The existence of fixed point theorems for partial q-set valued quasi-contractions in b-metric spaces and related results, Fixed Point Theory Appl. 2014 (2014), 226, 20 pages. [19] V. Lakshmikantham and L. Ciric, Coupled fixed point theorems for nonlinear contractions in partially ordered metric spaces, Nonlinear Anal., 70 (2009), 4341–4349. [20] N. Malhotra and B. Bansal, Some common coupled fixed point theorems for generalized contraction in b-metric spaces, J. Nonlinear Sci. Appl. 8 (2015), 8–16. [21] M. Olgun, O. Bicer and T. Alyildiz, A new aspect to Picard operators with simulation functions, Turk. J. Math. 40 (2016), 832–837. [22] N.S. Prasad, D.R. Babu and V.A. Babu, Common coupled fixed points of generalized contraction maps in b-metric spaces, Electron. J. Math. Anal. Appl. 9 (2021), no. 1, 131–150. [23] R.J. Shahkoohi and A. Razani, Some fixed point theorems for rational Geraghty contractive mappings in ordered-metric spaces, J. Inequal. Appl. 2014 (2014), no. 1, 1–23. [24] W. Shatanawi, Fixed and common fixed point for mappings satisfying some nonlinear contractions in b-metric spaces, J. Math. Anal. 7 (2016), no. 4, 1–12. [25] W. Shatanawi and M.B. Hani, A coupled fixed point theorem in b-metric spaces, Int. J. Pure Appl. Math. 109 (2016), no. 4, 889–897. [26] W. Shatanawi, B. Samet and M. Abbas, Coupled fixed point theorems for mixed monotone mappings in ordered partial metric spaces, Math. Comp. Model. 55 (2012), 680–687. | ||
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