DOI QR코드

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A FIXED POINT THEOREM ON PARTIAL METRIC SPACES SATISFYING AN IMPLICIT RELATION

  • Chang Il Kim (Department of Mathematics Education, Dankook University) ;
  • Gil Jun Han (Department of Mathematics Education, Dankook University)
  • 투고 : 2022.09.29
  • 심사 : 2023.01.15
  • 발행 : 2023.02.28

초록

Popa [14] proved the common fixed point theorem using implicit relations. Saluja [17] proved a fixed point theorem on complete partial metric spaces satisfying an implicit relation. In this paper, we prove a fixed point theorem on complete partial metric space satisfying another implicit relation.

키워드

과제정보

We appreciate the reviewers' valuable comments on our article. All of the reviewers' comments are helpful for us to improve our manuscript.

참고문헌

  1. I. Altun & K. Sadarangani: Generalized Geraghty type mappings on partial metric spaces and fixed point results. Arab J. Math. 2 (2013), 247-253. https://doi.org/10.1007/s40065-013-0073-2
  2. S. Banach: Surles operation dans les ensembles abstraits et leur application aux equation integrals. Fund. Math. 3 (1922), 133-181. https://doi.org/10.4064/fm-3-1-133-181
  3. M. Bukatin, R. Kopperman, S. Matthews & H. Pajoohesh: Partial metric spaces. Amer. Math. Monthly 116 (2009), 708-718. https://doi.org/10.4169/193009709X460831
  4. R.C. Dimri & G. Prasad: Coincidence theorems for comparable generalized non-linear contractions in ordered partial metric spaces. Comm. Korean Math. Soc. 32 (2017), no. 2, 375-387 https://doi.org/10.4134/CKMS.c160127
  5. D. Dukic, Z. Kadelburg & S. Radenovic: Fixed points of Geraghty-type mappings in various generalized metric spaces. Abstr. Appl. Anal. 2 (2011), 1-13. https://doi.org/10.1155/S1085337597000250
  6. E. Karapinar, W. Shatanawi & K. Tas: Fixed point theorems on partial metric spaces involving rational expressions. Miskolc Math. Notes 14 (2013), 135-142. https://doi.org/10.18514/mmn.2013.471
  7. S.G. Matthews: Partial metric topology. Research Report 212, Dept. of Computer Science, University of Warwick, 1992.
  8. S.G. Matthews: Partial metric topology. Proc. 8th Summer Conference on General Topology and its Applications, Ann. New York Acad. Sci. 728 (1994), 183-197.
  9. M. Nazam, M. Arshad & C. Park: Fixed point theorems for improved α-Geraghty contractions in partial metric spaces. J. Nonlinear Sci. Appl. 9 (2016), no.6, 4436-4449. https://doi.org/10.22436/jnsa.009.06.83
  10. S. Oltra & O. Valero. Banach's fixed theorem for partial metric spaces. Rend. Istit. Mat. Univ. Trieste 36 (2004) 17-26.
  11. D. Paesano & P. Vetro: Suzuki's type characterizations of completeness for partial metric spaces and fixed points for partially ordered metric spaces. Topology Appl. 159 (2012), 911-920. https://doi.org/10.1016/j.topol.2011.12.008
  12. C. Park, O.Z. Ege, S.A. Kumar, D.E. Jain & J.R. Lee: Fixed point theorems for various contraction conditions in digital metric spaces. J. Comput. Anal. Appl. 26 (2019), no. 8, 1451-1458
  13. C. Park & J.M. Rassias: Stability of the Jensen-type functional equation in C∗-algebras: A fixed point approach. Abstr. Appl. Anal. 2009 (2009), Article ID 360432
  14. V. Popa: Some fixed point theorems for compatible mappings satisfying an implicit relation. Demonstr. Math. 32 (1999), 157-164. https://doi.org/10.1515/dema-1999-0117
  15. G. Prasad & H. Isik: On solution of boundary value problems via weak contractions. J. Funct. Spaces 2022 (2022), Article ID 6799205
  16. G. Prasad & R.C. Dimri: Fixed point theorems via comparable mappings in ordered metric spaces. J. Anal. 27 (2019), no. 4, 1139-1150 https://doi.org/10.1007/s41478-019-00165-5
  17. G.S. Saluja: Some common fixed point theorems on partial metric spaces satisfying implicit relation. Math. Moravica 24 (2020), 29-43  https://doi.org/10.5937/matmor2001029s