Research article

Some theorems in partial metric space using auxiliary functions

  • Received: 10 January 2021 Accepted: 15 April 2021 Published: 21 April 2021
  • MSC : 47H10, 54H25

  • In the present manuscript, we establish some theorems for the existence and uniqueness of a fixed point in the framework of partial metric spaces using auxiliary functions. Our results generalize some existing results in the literature. To illustrate our results some examples are provided.

    Citation: Deepak Kumar, Sadia Sadat, Jung Rye Lee, Choonkil Park. Some theorems in partial metric space using auxiliary functions[J]. AIMS Mathematics, 2021, 6(7): 6734-6748. doi: 10.3934/math.2021396

    Related Papers:

  • In the present manuscript, we establish some theorems for the existence and uniqueness of a fixed point in the framework of partial metric spaces using auxiliary functions. Our results generalize some existing results in the literature. To illustrate our results some examples are provided.



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    [1] T. Abdeljawad, E. Karapinar, K. Taş, Existence and uniqueness of a common d = fixed point on partial metric spaces, Appl. Math. Lett., 24 (2011), 1900–1904. doi: 10.1016/j.aml.2011.05.014
    [2] H. Aydi, M. A. Barakat, E. Karapinar Z. D. Mitrović, T. Rashid, On $\mathcal{L}$-simulation mappings in partial metric spaces, AIMS Mathematics, 4 (2019), 1034–1045. doi: 10.3934/math.2019.4.1034
    [3] H. Aydi, C. M. Chen, E. Karapinar, Interpolative Ćirić-Reich-Rus type contractions via the Branciari distance, Mathematics, 7 (2019), 84. doi: 10.3390/math7010084
    [4] H. Aydi, E. Karapinar, A. F. Roldán López de Hierro, $\omega$-Interpolative Ćirić-Reich-Rus type contractions, Mathematics, 7 (2019), 57. doi: 10.3390/math7010057
    [5] S. Banach, Sur les op$\acute{e}$rations dans les ensembles abstraits et leur application aux $\acute{e}$quations int$\acute{e}$grales, Fund. Math., 3 (1922), 133–181. doi: 10.4064/fm-3-1-133-181
    [6] U. Y. Batsari, P. Kumam, S. Dhompongsa, Fixed points of terminating mappings in partial metric spaces, J. Fixed Point Theory Appl., 21 (2019), 39. doi: 10.1007/s11784-019-0672-4
    [7] S. Chandok, Some common fixed point results for rational type contraction mappings in partially ordered metric spaces, Math. Bohem., 138 (2013), 403–413.
    [8] S. Chandok, B. S. Choudhury, N. Metiya, Some fixed point results in ordered metric spaces for rational type expressions with auxiliary functions, J. Egypt. Math. Soc., 23 (2015), 95–101. doi: 10.1016/j.joems.2014.02.002
    [9] S. Chandok, S. Dinu, Common fixed points for weak $\psi$-contractive mappings in ordered metric spaces with applications, Abstr. Appl. Anal., 2013 (2013), 879084.
    [10] S. Chandok, J. Kim, Fixed point theorem in ordered metric spaces for generalized contractions mappings satisfying rational type expressions, J. Nonlinear Funct. Anal. Appl., 17 (2012), 301–306.
    [11] S. Chandok, D. Kumar, Some common fixed point results for rational type contraction mappings in complex valued metric spaces, J. Operator, 2013 (2013), 813707.
    [12] S. Chandok, D. Kumar, M. S. Khan, Some results in partial metric space using auxiliary functions, Appl. Math. E-Notes, 15 (2015), 233–242.
    [13] S. Chandok, T. D. Narang, M. A. Taoudi, Some common fixed point results in partially ordered metric spaces for generalized rational type contraction mappings, Vietnam J. Math., 41 (2013), 323–331. doi: 10.1007/s10013-013-0024-4
    [14] Y. U. Gaba, E. Karapinar, A new approach to the interpolative contractions, Axioms, 8 (2019), 110. doi: 10.3390/axioms8040110
    [15] P. Gautam, V. N. Mishra, R. Ali, S. Verma, Interpolative Chatterjea and cyclic Chatterjea contraction on quasi-partial $b$-metric space, AIMS Mathematics, 6 (2021), 1727–1742. doi: 10.3934/Math.2021103
    [16] R. Heckmann, Approximation of metric spaces by partial metric spaces, Appl. Categ. Struct., 7 (1999), 71–83. doi: 10.1023/A:1008684018933
    [17] E. Karapinar, A note on common fixed point theorems in partial metric spaces, Miskolc Math. Notes, 12 (2011), 185–191. doi: 10.18514/MMN.2011.335
    [18] E. Karapinar, Generalizations of Caristi Kirk's theorem on partial metric spaces, Fixed Point Theory Appl., 2011 (2011), 4. doi: 10.1186/1687-1812-2011-4
    [19] E. Karapinar, Fixed point theory for cyclic weak $\phi$-contraction, Appl. Math. Lett., 24 (2011), 822–825. doi: 10.1016/j.aml.2010.12.016
    [20] E. Karapinar, Revisiting the Kannan type contractions via interpolation, Adv. Theory Nonlinear Anal. Appl., 2 (2018), 85–87.
    [21] E. Karapinar, R. P. Agarwal, Interpolative Rus-Reich-Ćirić type contractions via simulation functions, An. Știinţ. Univ. "Ovidius" Constanţa Ser. Mat., 27 (2019), 137–152.
    [22] E. Karapinar, R. P. Agarwal, H. Aydi, Interpolative Reich-Rus-Ćirić type contractions on partial metric spaces, Mathematics, 6 (2018), 256. doi: 10.3390/math6110256
    [23] E. Karapinar, O. Alqahtani, H. Aydi, On interpolative Hardy-Rogers type contractions, Symmetry, 11 (2019), 8.
    [24] E. Karapinar, I. M. Erhan, Fixed point theorems for operators on partial metric spaces, Appl. Math. Lett., 24 (2011), 1894–1899. doi: 10.1016/j.aml.2011.05.013
    [25] E. Karapinar, W. Shatanawi, K. Taş, Fixed point theorem on partial metric spaces involving rational expressions, Miskolc Math. Notes, 14 (2013), 135–142. doi: 10.18514/MMN.2013.471
    [26] S. G. Matthews, Partial metric topology, University of Warwick, Research Report 212, 1992.
    [27] S. G. Matthews, Partial metric topology, In: Papers from the 8th Summer Conference at Queens College, New York, June 18–20, 1992, S. Andima (Ed.), New York: New York Acad. Sci., 1994, vol. 728,183–197.
    [28] S. Oltra, O. Velero, Banach's fixed point theorem for partial metric spaces, Rend. Istit. Mat. Univ. Trieste, XXXVI, (2004), 17–26.
    [29] R. Pant, R. Shukla, H. H. Nashine, R. Panicker, Some new fixed point theorems in partial metric spaces with application, J. Funct. Spaces, 2017 (2017), 1072750.
    [30] B. Samet, M. Rajović, R. Lazović, R. Stojiljković, Common fixed point results for nonlinear contractions in ordered partial metric spaces, Fixed Point Theory Appl., 2011 (2011), 71. doi: 10.1186/1687-1812-2011-71
    [31] W. Shatanawi, B. Samet, M. Abbas, Coupled fixed point theorems for mixed monotone mappings in ordered partial metric spaces, Math. Comput. Model., 55 (2012), 680–687. doi: 10.1016/j.mcm.2011.08.042
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