Title: A Note on Fixed Point Theory for Cyclic Weaker Meir-Keeler Function in Complete Metric Spaces
Author(s): Stojan Radenovic
Pages: 16-21
Cite as:
Stojan Radenovic, A Note on Fixed Point Theory for Cyclic Weaker Meir-Keeler Function in Complete Metric Spaces, Int. J. Anal. Appl., 7 (1) (2015), 16-21.

Abstract


In this paper we consider, discuss, improve and complement recent fixed points results for so-called cyclical weaker Meir-Keeler functions, established by Chi-Ming Chen [Chi-Ming Chen, Fixed point theory for the cyclic weaker Meir-Keeler function in complete metric spaces, Fixed Point Theory Appl., 2012, 2012:17]. In fact, we prove that weaker Meir-Keeler notion is superuous in results.

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References


  1. S. Banach, Sur les operations dans les ensembles abstraits et leur applications aux equations integrales, Fund. Math. 3 (1922) 133-181. Google Scholar

  2. M. A. Alghamdi, A. Petrusel and N. Shahzad, A fixed point theorem for cyclic generalized contractions in metric spaces, Fixed Point Theory Appl., 2012 (2012), Article ID 122. Google Scholar

  3. R. P. Agarwal, M. A. Alghamdi, D. O’Regan and N. Shahzad, Fixed point theory for cyclic weak Kannan type mappings, Journal of Indian Math. Soc. 81 (2014), 01-11. Google Scholar

  4. Chi-Ming Chen, Fixed point theory for the cyclic weaker Meir-Keeler function in complete metric spaces, Fixed Point Theory Appl., 2012 (2012), Article ID 17. Google Scholar

  5. M. S. Jovanovi´c, Generalized contractive mappings on compact metric spaces, Third mathematical conference of the Republic of Srpska, Trebinje 7 and 8 June 2013. Google Scholar

  6. E. Karapinar, Fixed point theory for cyclic weak φ−contraction, Appl. Math. Lett., 24 (2011) 822-825. Google Scholar

  7. E. Karapinar, K. Sadarangani, Corrigendum to ”Fixed point theory for cyclic weak φ−contraction” [Appl. Math. Lett. 24 (6)(2011) 822-825], Appl. Math. Lett., 25 (2012) 1582- 1584. Google Scholar

  8. S. Karpagam, S. Agarwal, Best proximity point theorems for cyclic orbital Meir-Keeler contractions maps, Nonlinear Anal., 74 (2011) 1040-1046. Google Scholar

  9. W. A. Kirk, P. S. Srinavasan, P. Veeramani, Fixed points for mapping satisfying cyclical contractive conditions, Fixed Point Theory 4 (2003), 79-89. Google Scholar

  10. L. Mili´cevi´c, Contractive families on compact spaces, arXiv:1312.0587v1 [math.MG], 2, December 2013. Google Scholar

  11. H. K. Nashine, Cyclic generalized ψ−weakly contractive mappings and fixed point results with applications to integral equations, Nonlinear Anal., 75 (2012) 6160-6169. Google Scholar

  12. H. K. Nashine, Z. Kadelburg, and P. Kumam, Implicit-Relation-Type Cyclic Contractive Mappings and Applications to Integral Equations, Abstr. Appl. Anal., 2012 (2012), Article ID 386253, 15 pages. Google Scholar

  13. M. Pacurar, Ioan A. Rus, Fixed point theory for cyclic ϕ−contractions, Nonlinear Anal., 72 (2010) 1181-1187. Google Scholar

  14. M. A. Petric, Some results concerning cyclical contractive mappings, General Math., 18 (2010), 213-226. Google Scholar

  15. S. Radenovi´c, Z. Kadelburg, D. Jandrli´c and A. Jandrli´c, Some results on weak contraction maps, Bull. Iranian Math. Soc. 38 (2012), 625-645. Google Scholar

  16. S. Radenovi´c, Some remarks on mappings satisfying cyclical contractive conditions, Fixed Point Theory Appl. submitted. Google Scholar

  17. S. Radenovi´c, A note on fixed point theory for cyclic ϕ−contractions, Demonstratio Matematica, submitted. Google Scholar

  18. S. Radenovic, Some results on cyclic generalized weakly C-contractions on partial metric spaces, in Bull. Allahabad Math. Soc. submitted. Google Scholar

  19. B. E. Rhoades, A comparison of various definitions of contractive mappings, Trans. Amer. Math. Soc. 226 (1977), 257-290. Google Scholar


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