DOI QR코드

DOI QR Code

SOME RESULTS ON BEST PROXIMITY POINT FOR CYCLIC B-CONTRACTION AND S-WEAKLY CYCLIC B-CONTRACTION MAPPINGS

  • V. Anbukkarasi (Department of Mathematics, Bharathidasan University) ;
  • R. Theivaraman (Department of Mathematics, Bharathidasan University) ;
  • M. Marudai (Department of Mathematics, Bharathidasan University) ;
  • P. S. Srinivasan (Department of Mathematics, Bharathidasan University)
  • 투고 : 2023.05.19
  • 심사 : 2023.08.22
  • 발행 : 2023.11.30

초록

The purpose of this paper is establish the existence of proximity point for the cyclic B-contraction mapping on metric spaces and uniformly convex Banach spaces. Also, we prove the common proximity point for the S-weakly cyclic B-contraction mapping. In addition, a few examples are provided to demonstrate our findings.

키워드

과제정보

All the authors are highly grateful to the editor and refree(s) for their valuable comments and suggestions for improving the paper.

참고문헌

  1. A. Anthony Eldred & P. Veeramani: Existence and convergence of best proximity points. J. Math. Anal. Appl. 323 (2006), 1001-1006. doi:10.1016/j.jmaa.2005.10.081 
  2. V. Sankar Raj: A best proximity point theorem for weakly contractive non-self-mappings. Nonlinear Analysis 74 (2011), 4804-4808. doi.org/10.1016/j.na.2011.04.052 
  3. W.A. Kirk, S. Reich & P. Veeramani: Proximinal retracts and best proximity pair theorems. Numer. Funct. Anal. Optim. 24 (2003), 851-862. doi:10.1081/NFA-120026380 
  4. R. Theivaraman, P.S. Srinivasan, S. Thenmozhi & S. Radenovic: Some approximate fixed point results for various contraction type mappings. Adv. Fixed Point Theory. 13 (2023), 1-20. https://doi.10.28919/afpt/8080 
  5. S. Sadiq Basha & N. Shahzad: Best proximity point theorems for generalized proximal contractions. Fixed Point Theory and Applications. doi:10.1186/1687-1812-2012-42 
  6. A. Al-Thahafi & N. Shahzad: Convergence and existence for best proximity points. Nonlinear Analysis. 70 (2009), 3665-3671. doi:10.1016/j.na.2008.07.022 
  7. A. Antony Eldred & P. Veeramani: Proximal pointwise contraction. Topology and its Applications. 156 (2009), 2942-2948.  https://doi.org/10.1016/j.topol.2009.01.017
  8. S. Karpagam & Sushama Agrawal: Best proximity points theorems for cyclic Meir-Keeler contraction maps. Nonlinear Analysis. doi:10.1016/j.na.2010.07.026 
  9. W.A. Kirk, P.S. Srinavasan & P. Veeramani: Fixed Points for mapping satisfying cylical contractive conditions. Fixed Point Theory. 4 (2003), 79-89. http://www.math.ubbcluj.ro/ nodeacj/journal.htm 
  10. G. Petrushel: Cyclic representations and periodic points. Studia Univ. Babes-Bolyai. Math. 50 (2005), 107-112. 
  11. M. Pacurar & I.A. Rus: Fixed point theory for cyclic ϕ-contractions. Nonlinear Anal. 72 (2010), no. 3-4, 1181-1187. doi:10.1016/j.na.2009.08.0024 
  12. M. Marudai & V.S. Bright: Unique fixed point theorem weakly B-contractive mappings. Far East journal of Mathematical Sciences (FJMS). 98 (2015), no. 7, 897-914. http://dx.doi.org/10.17654/FJMSDec2015-897-914 
  13. Naeem Abbas, Mujahid Abbas & Sadiq Farooq: Best proximity point results in generalized metric spaces. Thai Journal of mathematics. 20 (2022), no. 2, 589-603. http://thaijmath.in.cmu.ac.th 
  14. L.N. Mishra, V. Dewangan, V.N. Mishra & S. Karateked: Best proximity points of admissible almost generalized weakly contractive mappings with rational expressions on b-metric spaces. J. Math. Comput. Sci. 22 (2021), 97-109. http://dx.doi.org/10.22436/jmcs.022.02.01 
  15. A.A. Khan & B. Ali: Completeness of b-metric spaces and best proximity points of quasi-contractions. Symmetry 13 (2021), 2206. http://doi.org/0.3390/sym13112206 
  16. A.A. Khan, B. Ali, T. Nazir & M. De la Sen: Completeness of metric space and existence of best proximity points. AIMS Math. 7 (2022), 7318-7336. doi:10.3934/math.2022408 
  17. M. Aslantas, H. Sahin & I. Altun: Best proximity point theorems for cyclic p-contractions with some consequences and applications. Non-linear Analysis, Model. Control. 26 (2021), 113-129. http://doi.org/10.15388/namc.2021.26.21415 
  18. I. Iqbal, N. Hussain & M.A. Kutbi: Existence of the solution to variational inequality, optimization problem, and elliptic boundary value problem through revisited best proximity point results. J. Comput. Appl. Math. 375 (2020), Article ID:112804. https://doi.org/10.1016/j.cam.2020.112804 
  19. A. Moussaoui, N. Hussain & S. Melliani: Global optimal solutions for proximal fuzzy contractions involving control functions. J. Math. (2021), Article ID 6269304. https://doi.org/10.1155/2021/6269304 
  20. A. Moussaoui, V. Todorcevic, M. Pantovic, S. Radenovi'c & S. Melliani: Fixed Point Results via G-Transitive Binary Relation and Fuzzy L-R-Contraction. Mathematics, (2023). https://doi.org/10.3390/math11081768