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COINCIDENCE POINT RESULTS UNDER GERAGHTY-TYPE CONTRACTION

  • Amrish Handa (Department of Mathematics, Govt. P. G. Arts and Science College)
  • Received : 2024.04.09
  • Accepted : 2024.06.21
  • Published : 2024.08.31

Abstract

The main aim of this research article is to establish some coincidence point theorem for G-non-decreasing mappings under Geraghty-type contraction on partially ordered metric spaces. Furthermore, we derive some multidimensional results with the help of our unidimensional results. Our results improve and generalize various well-known results in the literature.

Keywords

References

  1. S.A. Al-Mezel, H. Alsulami, E. Karapinar & A. Roldan: Discussion on multidimensional coincidence points via recent publications. Abstr. Appl. Anal. 2014 (2014), Article ID 287492. https://doi.org/10.1155/2014/287492
  2. M. Berzig & B. Samet: An extension of coupled fixed points concept in higher dimension and applications. Comput. Math. Appl. 63 (2012), no. 8, 1319-1334. https://doi.org/10.1016/j.camwa.2012.01.018
  3. B. Deshpande & A. Handa: Coincidence point results for weak 𝜓 - 𝜙 contraction on partially ordered metric spaces with application. Facta Universitatis Ser. Math. Inform. 30 (2015), no. 5, 623-648.
  4. B. Deshpande & A. Handa: On coincidence point theorem for new contractive condition with application. Facta Universitatis Ser. Math. Inform. 32 (2017), no. 2, 209-229. https://doi.org/10.22190/FUMI1702209D
  5. B. Deshpande & A. Handa: Multidimensional coincidence point results for generalized (𝜓, 𝜃, 𝜑)-contraction on ordered metric spaces. J. Nonlinear Anal. Appl. 2017 (2017), no. 2, 132-143. https://doi.org/10.5899/2017/jnaa-00314
  6. B. Deshpande & A. Handa: Utilizing isotone mappings under Geraghty-type contraction to prove multidimensional fixed point theorems with application. J. Korean Soc. Math. Educ. Ser. B: Pure Appl. Math. 25 (2018), no. 4, 279-295. https://doi.org/10.7468/jksmeb.2018.25.4.279
  7. B. Deshpande, A. Handa & S.A. Thoker: Existence of coincidence point under generalized nonlinear contraction with applications. East Asian Math. J. 32 (2016), no. 3, 333-354. https://doi.org/10.7858/eamj.2016.025
  8. I.M. Erhan, E. Karapinar, A. Roldan & N. Shahzad: Remarks on coupled coincidence point results for a generalized compatible pair with applications. Fixed Point Theory Appl. 2014 (2014), Paper No. 207. https://doi.org/10.1186/1687-1812-2014-207
  9. M. Geraghty: On contractive mappings. Proc. Amer. Math. Soc. 40 (1973), 604-608.
  10. A. Handa: Multidimensional coincidence point results for contraction mapping principle. J. Korean Soc. Math. Educ. Ser. B: Pure Appl. Math. 26 (2019), no. 4, 277-288. https://doi.org/10.7468/jksmeb.2019.26.4.277
  11. A. Handa, R. Shrivastava & V.K. Sharma: Multidimensional coincidence point results for generalized (𝜓, 𝜃, 𝜑)-contraction on partially ordered metric spaces. Pramana Research Journal 9 (2019), no. 3, 708-720. https://www.pramanaresearch.org/gallery/prj-p641.pdf
  12. A. Handa, R. Shrivastava & V.K. Sharma: Multidimensional coincidence point results for new contractive condition on partially ordered metric spaces. The International J. Anal. and Experimental Modal Anal. XI (2019) no. IX, 3820-3832. https://doi.org/18.0002.IJAEMA.2019.V11I9.208301.3586
  13. A. Handa, R. Shrivastava & V.K. Sharma: Multidimensional coincidence point theorem under Mizoguchi-Takahashi contraction on partially ordered metric spaces, J. Inform. Comput. Sci. 9 (2019), no. 10, 811-827. https://joics.org/VOL-9-ISSUE-10-2019 10-2019
  14. Z. Kadelburg, P. Kumam, S. Radenovic & W. Sintunavarat: Common coupled fixed point theorems for Geraghty-type contraction mappings using monotone property. Fixed Point Theory Appl. 2015 (2015), Paper No. 27. https://doi.org/10.1186/s13663-015-0278-5
  15. E. Karapinar, A. Roldan, J. Martinez-Moreno & C. Roldan: Meir-Keeler type multidimensional fixed point theorems in partially ordered metric spaces. Abstr. Appl. Anal. 2013 (2013), Article ID 406026. https://dx.doi.org/10.1155/2013/406026
  16. E. Karapinar, A. Roldan, N. Shahzad & W. Sintunavarat: Discussion on coupled and tripled coincidence point theorems for φ-contractive mappings without the mixed g-monotone property. Fixed Point Theory Appl. 2014 (2014), Paper No. 92. https://doi.org/10.1186/1687-1812-2014-92
  17. A. Roldan & E. Karapinar: Some multidimensional fixed point theorems on partially preordered G*-metric spaces under (𝜓, 𝜑)-contractivity conditions. Fixed Point Theory Appl. 2013 (2013), Paper No. 158. https://doi.org/10.1186/1687-1812-2013-158
  18. A. Roldan, J. Martinez-Moreno & C. Roldan: Multidimensional fixed point theorems in partially ordered metric spaces. J. Math. Anal. Appl. 396 (2012), 536-545. https://doi.org/10.1016/j.jmaa.2012.06.049
  19. A. Roldan, J. Martinez-Moreno, C. Roldan & E. Karapinar: Multidimensional fixed-point theorems in partially ordered complete partial metric spaces under (𝜓, 𝜑)-contractivity conditions. Abstr. Appl. Anal. 2013 (2013), Article ID 634371. https://dx. doi.org/10.1155/2013/634371
  20. A. Roldan, J. Martinez-Moreno, C. Roldan & E. Karapinar: Some remarks on multidimensional fixed point theorems. Fixed Point Theory 15 (2014), no. 2, 545-558.
  21. F. Shaddad, M.S.M. Noorani, S.M. Alsulami & H. Akhadkulov: Coupled point results in partially ordered metric spaces without compatibility. Fixed Point Theory Appl. 2014 (2014), Paper No. 204. https://doi.org/10.1186/1687-1812-2014-204
  22. S. Wang: Coincidence point theorems for G-isotone mappings in partially ordered metric spaces. Fixed Point Theory Appl. 2013 (2013), Paper No. 96. https://doi.org/10.1186/1687-1812-2013-96
  23. S. Wang: Multidimensional fixed point theorems for isotone mappings in partially ordered metric spaces. Fixed Point Theory Appl. 2014 (2014), Paper No. 137. https://doi.org/10.1186/1687-1812-2014-137