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Common fixed point theorems on complex valued extended $ b $-metric spaces for rational contractions with application

  • Received: 17 August 2022 Revised: 15 September 2022 Accepted: 19 September 2022 Published: 20 October 2022
  • MSC : 37C25, 47H10, 54H25

  • The purpose of this article is to establish common fixed point results on complex valued extended $ b $-metric spaces for the mappings satisfying rational expressions on a closed ball. Our investigations generalize some well-known results of literature. Furthermore, we supply a significant example to show the authenticity of established results. As application, we solve Urysohn integral equations by our main results.

    Citation: Amer Hassan Albargi. Common fixed point theorems on complex valued extended $ b $-metric spaces for rational contractions with application[J]. AIMS Mathematics, 2023, 8(1): 1360-1374. doi: 10.3934/math.2023068

    Related Papers:

  • The purpose of this article is to establish common fixed point results on complex valued extended $ b $-metric spaces for the mappings satisfying rational expressions on a closed ball. Our investigations generalize some well-known results of literature. Furthermore, we supply a significant example to show the authenticity of established results. As application, we solve Urysohn integral equations by our main results.



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    [1] A. Azam, B. Fisher, M. Khan, Common fixed point theorems in complex valued metric spaces, Num. Funct.Anal. Optimiz., 32 (2011), 243–253. https://doi.org/10.1080/01630563.2011.533046 doi: 10.1080/01630563.2011.533046
    [2] F. Rouzkard, M. Imdad, Some common fixed point theorems on complex valued metric spaces, Comput. Math. Appl., 64 (2012), 1866–1874. https://doi.org/10.1016/j.camwa.2012.02.063 doi: 10.1016/j.camwa.2012.02.063
    [3] W. Sintunavarat, P. Kumam, Generalized common fixed point theorems in complex valued metric spaces and applications, J. Inequl. Appl., 2012 (2012), 84. https://doi.org/10.1186/1029-242X-2012-84 doi: 10.1186/1029-242X-2012-84
    [4] K. Sitthikul, S. Saejung, Some fixed point theorems in complex valued metric spaces, Fixed Point Theory Appl., 2012 (2012), 189. https://doi.org/10.1186/1687-1812-2012-189 doi: 10.1186/1687-1812-2012-189
    [5] J. Ahmad, C. Klin-Eeam, A. Azam, Common fixed points for multivalued mappings in complex valued metric spaces with applications, Abstr. Appl. Anal., 2013 (2013), 854965. https://doi.org/10.1155/2013/854965 doi: 10.1155/2013/854965
    [6] A. Azam, J. Ahmad, P. Kumam, Common fixed point theorems for multi-valued mappings in complex-valued metric spaces, J. Inequl. Appl., 2013 (2013), 578. https://doi.org/10.1186/1029-242X-2013-578 doi: 10.1186/1029-242X-2013-578
    [7] C. Klin-Eam, C. Suanoom, Some common fixed point theorems for generalized contractive type mappings on complex valued metric spaces, Abstr. Appl. Anal., 2013 (2013), 604215. https://doi.org/10.1155/2013/604215 doi: 10.1155/2013/604215
    [8] M. K. Kutbi, J. Ahmad, A. Azam, N. Hussain, On fuzzy fixed points for fuzzy maps with generalized weak property, J. Appl. Math., 2014 (2014), 1–12. https://doi.org/10.1155/2014/549504 doi: 10.1155/2014/549504
    [9] M. Humaira, G. Sarwar, N. V. Kishore, Fuzzy fixed point results for $\varphi $ contractive Mapping with applications, Complexity, 2018 (2018), 5303815. https://doi.org/10.1155/2018/5303815 doi: 10.1155/2018/5303815
    [10] Humaira, M. Sarwar, P. Kumam, Common fixed point results for fuzzy mappings on complex-valued metric spaces with homotopy results, Symmetry, 11 (2019), 61. https://doi.org/10.3390/sym11010061 doi: 10.3390/sym11010061
    [11] A. A. Mukheimer, Some common fixed point theorems in complex valued $b$-metric spaces, Sci. World J., 2014 (2014), 587825. https://doi.org/10.1155/2014/587825 doi: 10.1155/2014/587825
    [12] S. Vashistha, J. Kumar, Common fixed point theorem for generalized contractive type paps on complex valued $b$-metric spaces, Int. J. Math. Anal., 9 (2015), 2327–2334. https://doi.org/10.12988/ijma.2015.57179 doi: 10.12988/ijma.2015.57179
    [13] K. P. Rao, N. Nagar, J. R. Prasad, A common fixed point theorem in complex valued $b$-metric spaces, Bull. Math. Stat. Res., 1 (2013), 1–8.
    [14] N. Ullah, M. S. Shagari, A. Azam, Fixed point theorems in complex valued extended $b$-metric spaces, Moroccan J. Pure. Appl. Anal., 5 (2019), 140–163. https://doi.org/10.2478/mjpaa-2019-0011 doi: 10.2478/mjpaa-2019-0011
    [15] A. H. Albargi, J. Ahmad, Common $\alpha $-fuzzy fixed point results for Kannan type contractions with application, J. Func. Spaces, 2022 (2022), 1–9. https://doi.org/10.1155/2022/5632119 doi: 10.1155/2022/5632119
    [16] R. J. C. Pushpa, A. A. Xavier, J. M. Joseph, M. Marudai, Common fixed point theorems under rational contractions in complex valued extended $b$-metric spaces, Int. J. Nonlinear Anal. Appl., 13 (2022), 3479–3490. https://doi.org/10.22075/IJNAA.2020.20025.2118 doi: 10.22075/IJNAA.2020.20025.2118
    [17] N. Ullah, M. S. Shagari, A. Tahir, A. U. Khan, Common fixed point theorems in complex valued non-negative extended $b$-metric space, J. Anal. Appl. Math., 2021 (2021), 35–47. https://doi.org/10.2478/ejaam-2021-0004 doi: 10.2478/ejaam-2021-0004
    [18] N. Ullah, M. S. Shagari, Fixed point results in complex valued extended $b$-metric spaces and related applications, Annal. Math. Comput. Sci., 1 (2021).
    [19] A. E. Shammaky, J. Ahmad, A. F. Sayed, On fuzzy fixed point results in complex valued extended $b$-metric spaces with application, J. Math., 2021 (2021), 9995897. https://doi.org/10.1155/2021/9995897 doi: 10.1155/2021/9995897
    [20] R. P. Agarwal, E. Karapınar, D. O'Regan, A. F. Roldán-López-de-Hierro, Fixed point theory in metric type spaces, Springer, 2015.
    [21] P. Debnath, N. Konwar, S. Radenović, Metric fixed point theory: Applications in science, engineering and behavioural sciences, Springer Verlag, 2021. https://doi.org/10.1007/978-981-16-4896-0
    [22] S. Aleksić, Z. Kadelburg, Z. D. Mitrovíć, S. N. Radenović, A new survey: Cone metric spaces, arXiv, 2018. https://doi.org/10.48550/arXiv.1805.04795
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