DOI QR코드

DOI QR Code

MULTIDIMENSIONAL COINCIDENCE POINT RESULTS FOR CONTRACTION MAPPING PRINCIPLE

  • Handa, Amrish (Department of Mathematics, Govt. P. G. Arts and Science College)
  • 투고 : 2019.07.17
  • 심사 : 2019.10.05
  • 발행 : 2019.11.30

초록

The main objective of this article is to establish some coincidence point theorem for g-non-decreasing mappings under contraction mapping principle on a partially ordered metric space. Furthermore, we constitute multidimensional results as a simple consequences of our unidimensional coincidence point theorem. Our results improve and generalize various known results.

키워드

참고문헌

  1. S.A. Al-Mezel, H. Alsulami, E. Karapinar & A. Roldan: Discussion on multidimen-sional coincidence points via recent publications. Abstr. Appl. Anal. 2014, Article ID 287492.
  2. S.M. Alsulami: Some coupled coincidence point theorems for a mixed monotone operator in a complete metric space endowed with a partial order by using altering distance functions. Fixed Point Theory Appl. 2013, 194.
  3. M. Berzig & B. Samet: An extension of coupled fixed point's concept in higher dimen-sion and applications. Comput. Math. Appl. 63 (2012), no. 8, 1319-1334. https://doi.org/10.1016/j.camwa.2012.01.018
  4. B. Deshpande & A. Handa: Coincidence point results for weak ${\psi}$ - ${\varphi}$ contraction on partially ordered metric spaces with application. Facta Universitatis Ser. Math. Inform. 30 (2015), no. 5, 623-648.
  5. 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
  6. 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
  7. B. Deshpande & A. Handa: Multidimensional coincidence point results for generalized $({\psi},{\theta},{\varphi})$-contraction on ordered metric spaces. J. Nonlinear Anal. Appl. 2017 (2017), no. 2, 132-143. https://doi.org/10.5899/2017/jnaa-00314
  8. B. Deshpande & A. Handa: Utilizing isotone mappings under Geraghty-type contrac-tion to prove multidimensional fixed point theorems with application. J. Korean Soc. Math. Educ. Ser. B: Pure Appl. Math. 25 (2018), no. 4, 279-95.
  9. A. Handa, R. Shrivastava & V.K. Sharma: Multidimensional coincidence point results for generalized $({\psi},{\theta},{\varphi})$ -contraction on partially ordered metric spaces. Pramana Research Journal 9 (2019), no. 3, 708-20.
  10. 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, 207.
  11. E. Karapinar, A. Roldan, C. Roldan & J. Martinez-Moreno: A note on N-Fixed point theorems for nonlinear contractions in partially ordered metric spaces. Fixed Point Theory Appl. 2013, Article ID 310.
  12. E. Karapinar, A. Roldan, J. Martinez-Moreno & C. Roldan: Meir-Keeler type multi-dimensional fixed point theorems in partially ordered metric spaces. Abstr. Appl. Anal. 2013, Article ID 406026.
  13. E. Karapinar, A. Roldan, N. Shahzad & W. Sintunavarat: Discussion on coupled and tripled coincidence point theorems for ${\phi}$-contractive mappings without the mixed g-monotone property. Fixed Point Theory Appl. 2014, Article ID 92.
  14. A. Razani & V. Parvaneh: Coupled coincidence point results for $({\psi},{\alpha},{\beta})$-weak contractions in partially ordered metric spaces. J. Appl. Math. 2012, Article ID 496103.
  15. 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
  16. A. Roldan & E. Karapinar: Some multidimensional fixed point theorems on partially preordered $G^{\ast}$ -metric spaces under $({\psi},{\varphi})$ -contractivity conditions. Fixed Point Theory Appl. 2013, Article ID 158.
  17. A. Roldan, J. Martinez-Moreno, C. Roldan & E. Karapinar: Multidimensional fixed-point theorems in partially ordered complete partial metric spaces under $({\psi},{\varphi})$ -contractivity conditions. Abstr. Appl. Anal. 2013, Article ID 634371.
  18. A. Roldan, J. Martinez-Moreno, C. Roldan & E. Karapinar: Some remarks on multi-dimensional fixed point theorems. Fixed Point Theory 15 (2014), no. 2, 545-558.
  19. B. Samet, E. Karapinar, H. Aydi & V.C. Rajic: Discussion on some coupled fixed point theorems. Fixed Point Theory Appl. 2013, 50.
  20. 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, 204.
  21. Y. Su: Contraction mapping principle with generalized altering distance function in ordered metric spaces and applications to ordinary differential equations. Fixed Point Theory Appl. 2014, 227.
  22. S.Wang: Coincidence point theorems for G-isotone mappings in partially ordered metric spaces. Fixed Point Theory Appl. 2013, 96.
  23. S. Wang: Multidimensional fixed point theorems for isotone mappings in partially ordered metric spaces. Fixed Point Theory Appl. 2014, 137.