Three-point fixed point results in \(b\)-metric spaces
The paper was RETRACTED due to irreparable mistakes and confirmation of the editor-in-chief.
Keywords:
Fixed point, b-metric, mappings contracting perimeters of trianglesAbstract
In this paper, we explore fixed-point theorems in b-metric spaces, focusing on mappings that contract the perimeters of triangles and their generalizations. We establish new fixed-point results for such mappings under specific conditions, demonstrating their existence and uniqueness in b-metric spaces. Additionally, we introduce three-point Kannan-type generalized mappings, extending classical fixed-point theorems to a broader context. These results not only generalize existing theorems but also open new directions for further research in fixed-point theory within the b-metric framework.
References
[1] S. Banach, Sur les op´erations dans les ensembles abstraits et leur application aux ´equations int´egrales, Fundamenta Mathematicae 3 (1922), 133-181.
[2] V. Berinde, M. Pacurar, The early developments in fixed point theory on b-metric spaces: a brief survey and some important related aspects, Carpathian J. Math. 38 (2022), 523-538.
[3] R. Bisht, E. Petrov, A three point extension of Chatterjea’s fixed point theorem with at most two fixed points, arXiv:2403.07906.
[4] M. Boriceanu, M. Bota, A. Petrusel, Multivalued fractals in b-metric spaces, Cent. Eur. J. Math. 8 (2010), 367-377.
[5] S. Czerwik, Contraction mappings in b-metric spaces, Acta Math. Inform. Univ. Ostrav. 1 (1993), 5-11.
[6] S. Czerwik, K. Dlutek, S. Singh, Round-off stability of iteration procedures for set-valued operators in b-metric spaces, J. Natur. Phys. Sci. 11 (2007), 87-94.
[7] M. Jleli, B. Samet, C. Vetro, F. Vetro, Fixed points for multivalued mappings in b-metric spaces, Abstr. Appl. Anal. (2015), 718074.
[8] M. Jleli, C.M. Pacurar, B. Samet, New directions in fixed point theory in G-metric spaces and applications to mappings contracting perimeters of triangles, arXiv preprint (2024) arXiv:2405.11648.
[9] M. Jleli, C.M. Pacurar, B. Samet, Fixed point results for contractions of polynomial type, arXiv preprint (2024) arXiv:2406.03446
[10] R. Kannan, Some results on fixed points-II, Amer. Math. Monthly. 76 (1969), 405–408.
[11] E. Karapinar, A short survey on the recent fixed point results on b-metric spaces, Constr. Math. Anal. 1 (2018), 15–44.
[12] W. Kirk, N. Shahzad, b-Metric spaces. In: Fixed Point Theory in Distance Spaces, pp. 113-131. Springer, Berlin (2014).
[13] R. Miculescu, A. Mihail, New fixed point theorems for set-valued contractions in b-metric spaces, J. Fixed Point Theory Appl. 19 (2017), 2153–2163.
[14] C. Pacurar,O. Popescu, Fixed point theorem for generalized Chatterjea type mappings, Acta Mathematica Hungarica 173 (2), 500-509.
[15] C.M. Pacurar, O. Popescu, Fixed points for three point generalized orbital triangular contractions, arXiv preprint (2024) arXiv:2404.15682.
[16] E. Petrov, Fixed point theorem for mappings contracting perimeters of triangles, J. Fixed Point Theory Appl. 25 (2023) 1–11.
[17] E. Petrov, Periodic points of mappings contracting total pairwise distance, arXiv preprint (2024) arXiv:2402.02536.
[18] E. Petrov, R. K. Bisht, Fixed point theorem for generalized Kannan type mappings, Rendiconti del Circolo Matematico di Palermo Series 2 (2024), 1-18.
[19] O. Popescu, C.M. Pacurar, Mappings contracting triangles, arXiv preprint (2024) arXiv:2403.19488.
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