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Common Fixed Point Theorems for Generalized R′-contraction in b-metric Spaces

Received: 26 February 2022     Accepted: 8 April 2022     Published: 22 April 2022
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Abstract

In this paper, the researcher presents some common fixed point theorems for self-mappings satisfying generalized R′-contraction in b-metric spaces and obtained a unique common fixed point of a self-mapping satisfying certain contraction in the framework of b- metric spaces. The results presented over her generalize and extend some existing results in the literature. Finally, he illustrate example to support the results.

Published in Mathematics Letters (Volume 8, Issue 2)
DOI 10.11648/j.ml.20220802.11
Page(s) 22-31
Creative Commons

This is an Open Access article, distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution and reproduction in any medium or format, provided the original work is properly cited.

Copyright

Copyright © The Author(s), 2022. Published by Science Publishing Group

Keywords

Common Fixed Point, b-metric Space, R′-contraction, R′-function, Weakly Compatible Mapping, Simulation Function

References
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[2] A, F, Roldan Lopez de Hierro and Shahzad, (2015), New Fixed point theorems under R′-contractions, Fixed point theory and Applications, 98, 2015.
[3] I. A. Bakhatin, (1989), the contractive mapping principle in almost metric space, Func. Anal., 30, 26-37. 1, 1. 1.
[4] S. Czerwik, (1993), Contraction mapping in b-metric space, ActaMathematicaet Informatica University Ostraviensis, 1, 5-11.
[5] S. Phiangsungnoen and P. Kumamam, (2018), On stability of fixed point inclusion for multivalued type contraction mappings in dislocate b-metric space with application, Math ApplSci, 114, https://doi.org/10.1002/mma.4871.
[6] W, Kumam, P, Sukprasert, P. Kumam, A, Shoaib, A. Shahzad and Q. Mahmood, (2018), Some fuzzy fixed point results for fuzzy mappings in complete b-metric spaces, Cogent Mathematic sand Statistic, https://doi.org/10.1080/25742558.2018.1458933.
[7] T. Abdeljawad, E. Karapinar, K. Tas, Existence and uniqueness of a common fixed point on Partial metric spaces, Appl., math. Lett., 24 (2011), 1900-1904. 1.
[8] S. Phiangsunangnsungnoen and P. Kumamam, (2015), Fuzzy fixed point theorem for Mult-ivalued fuzzy contraction in b-metric spaces, J. Nonlinear Sci. Appl., 8, 5563.
[9] C. Mongkolcha, Y. J. Cho and P. Kumam, (2017), Fixed point theorems for simulation function in b-metric space via the wt-distance, Applied Genereal Topology, 18, 91-105.
[10] H. Piri and P. Kumam, (2016). Fixed point theoremsfor generalized F-Suzuki-Contraction in Complete b-metric spaces, Fixed Point Theory and Applications, 90, doi: 10.1186/s13663-016-0577-5.
[11] H. Aydi, A. Felhi, S. Sahmim, J. NonlinearSci Appl., 10 (2017), 1524-1537.1.
[12] A. Amin-Harandi, (2012). Metric space, partial metric space and fixed point theory Appl., 2012. 10.
[13] M. Pacurar, (2010). A sequence of almost contraction and fixed point in b-metric space, AnaleleUniversitati de Verst, T, Misora Seria Mathematica Information XLVIII, 3, 125-137.
[14] M. Boriceanu, (2009). Strict fixed point theorems for multivalued operations in b-metric Spaces, Int. J. Moda. math. 4, 285-301.
[15] A. Wiriyapongsanon and N. Phudolsitthiphat, (2018). Fixed point theorem for Generalized R-contraction in b-metric space, Chiang Mai University, Thai Journal of Math., 277-287.
[16] Jungck. G. and B. E. Rhoades, (2006). Fixed point theorems for occasionally weakly compatible mappings, fixed point theory 7 (2), 287-296.
[17] Jungck. G. (1985). Compatible mapping and common fixed points, Internet. J Math. Sci., 9, 771- 779.
[18] M. Aamri and D. EL Moutawakil, (2002). Some new common fixed point theorems under strict contractive conditions, J. Math. Anal., 270, 181-188.
[19] Boriceanu, M. and Bota, M. and Petrusel, A. (2010). Multivalued fractals in b-metric spaces, Cent. Eur. J. Math, 8 (2), 367-377.
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  • APA Style

    Soressa Wakesa Bekana. (2022). Common Fixed Point Theorems for Generalized R′-contraction in b-metric Spaces. Mathematics Letters, 8(2), 22-31. https://doi.org/10.11648/j.ml.20220802.11

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    ACS Style

    Soressa Wakesa Bekana. Common Fixed Point Theorems for Generalized R′-contraction in b-metric Spaces. Math. Lett. 2022, 8(2), 22-31. doi: 10.11648/j.ml.20220802.11

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    AMA Style

    Soressa Wakesa Bekana. Common Fixed Point Theorems for Generalized R′-contraction in b-metric Spaces. Math Lett. 2022;8(2):22-31. doi: 10.11648/j.ml.20220802.11

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  • @article{10.11648/j.ml.20220802.11,
      author = {Soressa Wakesa Bekana},
      title = {Common Fixed Point Theorems for Generalized R′-contraction in b-metric Spaces},
      journal = {Mathematics Letters},
      volume = {8},
      number = {2},
      pages = {22-31},
      doi = {10.11648/j.ml.20220802.11},
      url = {https://doi.org/10.11648/j.ml.20220802.11},
      eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.ml.20220802.11},
      abstract = {In this paper, the researcher presents some common fixed point theorems for self-mappings satisfying generalized R′-contraction in b-metric spaces and obtained a unique common fixed point of a self-mapping satisfying certain contraction in the framework of b- metric spaces. The results presented over her generalize and extend some existing results in the literature. Finally, he illustrate example to support the results.},
     year = {2022}
    }
    

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    AB  - In this paper, the researcher presents some common fixed point theorems for self-mappings satisfying generalized R′-contraction in b-metric spaces and obtained a unique common fixed point of a self-mapping satisfying certain contraction in the framework of b- metric spaces. The results presented over her generalize and extend some existing results in the literature. Finally, he illustrate example to support the results.
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Author Information
  • Department of Mathematics, Wollega University, Nekemte, Ethiopia

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