Fixed point theorems In controlled rectangular metric spaces. (English) Zbl 1520.54035
Summary: In this paper, we introduce an extension of rectangular metric spaces called controlled rectangular metric spaces, by changing the rectangular inequality in the definition of a metric space. We also establish some fixed point theorems for self-mappings defined on such spaces. Our main results extends and improves many results existing in the literature. Moreover, an illustrative example is presented to support the obtained results.
MSC:
| 54H25 | Fixed-point and coincidence theorems (topological aspects) |
| 54E40 | Special maps on metric spaces |
References:
| [1] | S. Anwar, M. Nazam, H. Al Sulami, A. Hussain, K. Javed & M. Arshad: Existence fixed-point theorems in the partial b-metric spaces and an application to the boundary value problem. AIMS Mathematics 7, no. 5, 8188-8205. doi:10.3934/math.2022456 |
| [2] | M. Asim, M. Imdad & S. Radenovic: Fixed point results in extended rectangular b-metric spaces with an application. UPB Sci. Bull. Ser. A 2019, 81, 11-20. · Zbl 1498.54054 |
| [3] | I. A. Bakhtin: The contraction mapping principle in quasimetric spaces. Funct. Anal., Unianowsk Gos. Ped. Inst. 30 (1989), 26-37. · Zbl 0748.47048 |
| [4] | S. Banach: Sur les operations dans les ensembles abstraits et leur application aux equations integrales. Fund. Math. 3 (1922), 133-181. · JFM 48.0201.01 · doi:10.4064/fm-3-1-133-181 |
| [5] | A. Branciari: A fixed point theorem of Banach-Caccioppoli type on a class of generalized metric spaces. Publ. Math. Debrecen 57 (2000), 31-37. · Zbl 0963.54031 · doi:10.5486/PMD.2000.2133 |
| [6] | S. Czerwik: Contraction mappings in b-metric spaces. Acta Math. Inform. Univ. Ostraviensis 1 (1993), 5-11. · Zbl 0849.54036 |
| [7] | M. Farhan, U. Ishtiaq, M. Saeed, A. Hussain & H. Al Sulami: Reich-Type and (α, F)-Contractions in Partially Ordered Double-Controlled Metric-Type Spaces with Applications to Non-Linear Fractional Differential Equations. Axioms 11, no. 10, 573. https://doi.org/10.3390/axioms11100573 |
| [8] | B. Fisher: Mappings satisfying a rational inequality. Bull. Math. Soc. Sci. Math. R. S. Roumanie (N.S.) 24 (1980), 247-251. · Zbl 0445.54028 |
| [9] | R. George, S. Radenovic, K. P. Reshma & S. Shukla: Rectangular b-metric space and contraction principles. J. Nonlinear Sci. Appl. 8 (2015), no. 6, 1005-1013. http://dx.doi.org/10.22436/jnsa.008.06.11 · Zbl 1398.54068 |
| [10] | R. Kannan: Some results on fixed points-II. Amer. Math. Monthly 76 (1969), 405-408. · Zbl 0179.28203 |
| [11] | A. Kari, M. Rossafi, E. Marhrani & M. Aamri: Fixed point theorem for Nonlinear F-contraction via w-distance. Advances in Mathematical Physics, vol. 2020, Article ID 6617517, 10 pages, 2020. https://doi.org/10.1155/2020/6617517 · Zbl 1477.54097 |
| [12] | A. Kari, M. Rossafi, H. Saffaj, E. Marhrani & M. Aamri: Fixed point theorems for θ-φ-contraction in generalized asymmetric metric spaces. Int. J. Math. Mathematical Sciences, (2020), Article ID 8867020. https://doi.org/10.1155/2020/8867020 · Zbl 1486.54059 |
| [13] | A. Kari, M. Rossafi, E. Marhrani & M. Aamri: New fixed point theorems for θ-φ-contraction on rectangular b-metric spaces. Abstract and Applied Analysis, vol. 2020, Article ID 8833214, 2020. https://doi.org/10.1155/2020/8833214 · Zbl 1474.54178 |
| [14] | A. Kari, M. Rossafi, E. Marhrani & M. Aamri: θ-φ-contraction on (α, η)-complete rectangular b-metric spaces. Int. J. Math. Mathematical Sciences, (2020), Article ID 5689458. https://doi.org/10.1155/2020/5689458 · Zbl 1480.54032 |
| [15] | W. A. Kirk & N. Shahzad: Generalized metrics and Caristi’s theorem. Fixed Point Theory Appl 2013, 129 (2013). https://doi.org/10.1186/1687-1812-2013-129 · Zbl 1295.54060 |
| [16] | N. Mlaiki, N. Dedovic, H. Aydi, M. G. Filipovic, B. Bin-Mohsin & S. Radenovic: Some New Observations on Geraghty and Ciric Type Results in b-Metric Spaces, Mathematics 7 (2019), Article ID 643. https://doi.org/10.3390/math7070643 |
| [17] | M. Nazam, Z. Hamid, H. Al Sulami & A. Hussain: Common Fixed-Point Theorems in the Partial b-Metric Spaces and an Application to the System of Boundary Value Problems, Journal of Function Spaces, vol. 2021, Article ID 7777754, 11 pages, 2021. https://doi.org/10.1155/2021/7777754 · Zbl 1489.54185 |
| [18] | S. Radenovic, T. Dosenovic, V. Ozturk & C. Dolicanin: A note on the paper: “Nonlinear integral equations with new admissibility types in b-metric spaces” J. Fixed Point Theory Appl. 19 (2017) 2287-2295. https://doi.org/10.1007/s11784-017-0416-2 · Zbl 1491.54135 |
| [19] | M. Rashid, L. Shahid, RP. Agarwal, A. Hussain & H. Al-Sulami: q-ROF mappings and Suzuki type common fixed point results in b-metric spaces with application. J Inequa.l Appl. 2022, 155 (2022). https://doi.org/10.1186/s13660-022-02894-x · Zbl 1532.54038 |
| [20] | S. Reich: Some remarks concerning contraction mappings. Canad. Math. Bull. 14 (1971), no. 2, 121-124. · Zbl 0211.26002 · doi:10.4153/CMB-1971-024-9 |
| [21] | M. Rossafi, A. Kari, C. Park & J. R. Lee: New fixed point theorems for θ-φ-contraction on b-metric spaces. J Math Comput SCI-JM. 29 (2023), no. 1, 12-27. http://dx.doi.org/10.22436/jmcs.029.01.02 |
| [22] | M. Rossafi, A. Kari & J. R. Lee: Best Proximity Point Theorems For Cyclic θ-φ-contraction on metric spaces. J. Korean Soc. Math. Educ. Ser. B: Pure Appl. Math. 29 (2022), no. 4, 335-352. https://doi.org/10.7468/jksmeb.2022.29.4.335 · Zbl 1520.54036 |
| [23] | M. Rossafi, A. Kari & J. R. Lee: Fixed Point Theorems For (φ; F)-Contraction in Generalized Asymmetric Metric Spaces. J. Korean Soc. Math. Educ. Ser. B: Pure Appl. Math. 29 (2022), no. 4, 369-399. https://doi.org/10.7468/jksmeb.2022.29.4.369 · Zbl 1520.54037 |
| [24] | J. R. Roshan, V. Parvaneh, Z. Kadelburg & N. Hussain: New fixed point results in b-rectangular metric spaces. Nonlinear Analysis: Modelling and Control 21 (2016), no. 5, 614-634. http://dx.doi.org/10.15388/NA.2016.5.4 · Zbl 1420.54089 |
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.
