10.30495/maca.2021.1929674.1010

Some coupled coincidence point results in partially ordered metric spaces

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  • Laya Fadakar1,
  • Hüseyin Işık2,
  • Shirin Tavakoli1,
  • Arezo Mardzad1,
  1. Department of Mathematics, Ardabil Branch, Islamic Azad University, Ardabil, Iran
  2. Department of Engineering Science, Bandırma Onyedi Eylül University, 10200 Bandırma, Balıkesir, Turkey

Published in Issue 2021-04-01

How to Cite

Some coupled coincidence point results in partially ordered metric spaces. (2021). Mathematical Analysis and Its Contemporary Applications, 3(2). https://doi.org/10.30495/maca.2021.1929674.1010

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Abstract

In this paper, we introduce the notion of partial-compatibility of mappings in an ordered partial metric space and use this notion to establish coupled coincidence point theorems for φ-mixed monotone mappings satisfying a nonlinear contraction condition. Our consequences is an extension of the results of Shatanawi et al. [W. Shatanawi, B. Samet and M. Abbas, Coupled fixed point theorems for mixed monotone mappings in ordered partial metric spaces, Math. Comp. Model., 55(3-4) (2012), 680-687]. We also provide an example to illustrate the results presented herein.

Keywords

  • Coupled coincidence point,
  • partially ordered set,
  • partial metric space,
  • mixed monotone property,
  • compatible mapping
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References

  1. T. Abdelljawad, E. Karapinar and K. Tas, Existence and uniqueness of common fixed point on partial metric spaces, Appl. Math. Lett., 24(2011), 1894-1899.
  2. I. Altun, A. Erduran, Fixed point theorems for monotone mappings on partial metric spaces, Fixed Point Theory Appl., 2011(2011), Article ID 508730
  3. I. Altun, F. Sola and H. Simsek, Generalized contractions on partial metric spaces, Topology Appl., 157(18)(2010), 2778-2785.
  4. A. H. Ansari, H. I¸sık and S. Radenovi´c, Coupled fixed point theorems for contractive mappings involving new function classes and applications, Filomat, 31(2017), 1893-1907.
  5. T. G. Bhaskar and V. Lakshmikantham, Fixed point theorems in partially ordered metric spaces and applications, Nonlinear Anal., 65(2006), 1379-1393.
  6. Lj. ´Ciri´c, B. Samet, H. Aydi and C. Vetro, Common fixed points of generalized contractions on partial metric spaces and an application, Appl. Math. Comp., 218(6)(2011), 2398-2406.
  7. B. S. Choudhury and A. Kundu, A coupled coincidence point result in partially ordered metric spaces for compatible mappings, Nonlinear Anal., 73 (2010), 2524-2531.
  8. D. Ili´c, V. Pavlovi´c and V. Rakocevi´c, Extensions of the Zamfirescu theorem to partial metric spaces, Math. Comp. Model., 55(3-4)(2011), 801-809.
  9. D. Ili´c, V. Pavlovi´c and V. Rakocevi´c, Some new extensions of Banach's contraction principle to partial metric space, Appl. Math. Lett., 24(2011), 1326-1330.
  10. H. I¸sık, Solvability to coupled systems of functional equations via fixed point theory, TWMS J. App. Eng. ath., 8(2018), 230-237.
  11. H. I¸sık and C. Park, Existence of a common solution to systems of integral equations via fixed point results, Open Math., 18(1)(2020), 249-261.
  12. H. I¸sık and S. Radenovi´c, A new version of coupled fixed point results in ordered metric spaces with applications, UPB Sci. Bull. Ser. A, 79(2017), 131-138.
  13. H. I¸sık and W. Sintunavarat, An investigation of the common solutions for coupled systems of functional equations arising in dynamic programming, Math. 7(10) (2019),
  14. H. I¸sık and D. Turkoglu, Coupled fixed point theorems for new contractive mixed monotone mappings and applications to integral equations, Filomat, 28(2014), 1253-1264.
  15. E. Karapinar, Generalizations of Caristi Kirk's theorem on partial metric spaces, Fixed Point Theory Appl., 2011(2011).
  16. E. Karapinar and I. M. Erhan, Fixed point theorems for operators on partial metric spaces, Appl. Math. Lett., 24(2011), 1900-1904.
  17. V. Lakshmikantham and L. Ciric, Coupled fixed point theorems for nonlinear contractions in partially ordered metric spaces, Nonlinear Anal., 70(12)(2009), 4341-4349.
  18. S. G. Matthews, Partial metric topology, General Topology and its Applications. Proc. 8th Summer Conf., Queen's College, 1992, in: Ann. New York Acad. Sci., 728(1994), 183-197.
  19. W. Shatanawi, B. Samet and M. Abbas, Coupled fixed point theorems for mixed monotone mappings in ordered partial metric spaces, Math. Comp. Model., 55(3-4)(2012), 680-687.