Some fixed point-type results for a class of extended cyclic self-mappings with a more general contractive condition

Fixed Point Theory and Applications

Volumn 2011, Issue , 2011, Pages

  De La Sen, M ^a   Agarwal, Ravi P ^b  

^a UNIVERSITY OF THE BASQUE COUNTRY UPV EHU   (Spain)

^b TEXAS A AND M UNIVERSITY KINGSVILLE   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 84894105581     PISSN: 16871820     EISSN: 16871812     Source Type: Journal    
DOI: 10.1186/1687-1812-2011-59     Document Type: Article

References (29)

1. Harjani, J, Lopez, B, Sadarangani, K: A fixed point theorem for mappings satisfying a contractive condition of rational type of partially ordered metric space. Abstr Appl Anal 2010, 8 (2010). (Article Number 190701)
2. Harjani, J, Sadarangani, K: Fixed point theorems for weakly contractive mappings in partly ordered sets. Nonlinear Anal Theory Methods Appl. 71(7-8), 3403-3410 (2009). doi:10.1016/j.na.2009.01.240
3. Bhardwaj, R, Rajput, SS, Yadava, RN: Application of fixed point theory in metric spaces. Thai J Math. 5(2), 253-259 (2007)
4. Enjouji, Y, Nakanishi, M, Suzuki, T: A generalization of Kannan's fixed point theorem. Fixed Point Theory Appl 2009, 10 (2009). (Article Number 192872)
5. Banach, S: Sur les operations dans les ensembles abstracts et leur application aux équations intégrales. Fundamenta Mathematicae. 3, 133181 (1922)
6. Chatterjee, SK: Fixed point theorems. Comptes Ren Acad Bulgaria Sci. 25, 727730 (1972)
7. Fisher, B: A fixed point theorem for compact metric spaces. Publ Math Debrecen. 25, 193194 (1978)
8. Kannan, R: Some results on fixed points. Bull Calcutta Math Soc. 60, 7176 (1968)
9. Kannan, R: Some results on fixed points-II. Am Math Monthly. 76, 405408 (1969)
10. Reich, S: Some remarks concerning contraction mappings. Can Math Bull. 14, 121124 (1971)
11. Kikkawa, M, Suzuki, T: Some similarity between contractions and Kannan mappings. Fixed Point Theory Appl 2008, 8 (2008). (Article ID 649749)
12. Subrahmanyam, PV: Completeness and fixed points. Monatshefte für Mathematik. 80(4), 325-330 (1975). doi:10.1007/BF01472580
13. Kirk, WA, Srinivasan, PS, Veeramani, P: Fixed points for mappings satisfying cyclical contractive conditions. Fixed Point Theory. 4(1), 79-89 (2003)
14. Eldred, AA, Veeramani, P: Existence and convergence of best proximity points. J Math Anal Appl. 323(2), 1001-1006 (2006). doi:10.1016/j.jmaa.2005.10. 081
15. Karpagam, S, Agrawal, S: Best proximity point theorems for p-cyclic Meir-Keeler contractions. Fixed Point Theory Appl 2009, 9 (2009). (Article Number 197308)
16. Di Bari, S, Suzuki, T, Vetro, C: Best proximity points for cyclic Meir-Keeler contractions. Nonlinear Anal.: Theory Methods Appl. 69(11), 3790-3794 (2008). doi:10.1016/j.na.2007.10.014
17. De la Sen, M: Linking contractive self-mappings and cyclic Meir-Keeler contractions with Kannan self-mappings. Fixed Point Theory Appl 2010, 23 (2010). (Article Number 572057)
18. De la Sen, M: Some combined relations between contractive mappings, Kannan mappings reasonable expansive mappings and T-stability. Fixed Point Theory Appl 2009, 25 (2009). (Article Number 815637)
19. Kikkawa, M, Suzuki, T: Three fixed point theorems for generalized contractions with constants in complete metric spaces. Nonlinear Anal: Theory Methods Appl. 69(9), 2942-2949 (2008). doi:10.1016/j.na.2007.08.064
20. Suzuki, T: Some notes on Meir-Keeler contractions and L-functions. Bull Kyushu Inst Technol. 53, 1213 (2006)
21. Derafshpour, M, Rezapour, S, Shahzad, N: On the existence of best proximity points of cyclic contractions. Adv Dyn Syst Appl. 6(1), 33-40 (2011)
22. Rezapour, Sh, Derafshpour, M, Shahzad, N: Best proximity points of cyclic φ-contractions on reflexive Banach spaces. Fixed Point Theory Appl 2010, 7 (2010). (Article ID 946178)
23. Qin, X, Kang, SM, Agarwal, RP: On the convergence of an implicit iterative process for generalized asymptotically quasi non-expansive mappings. Fixed Point Theory Appl 2010, 19 (2010). (Article Number 714860)
24. Rus, IA: Cyclic representations and fixed points. Ann T Popoviciu Seminar Funct Eq Approx Convexity. 3, 171178 (2005)
25. Pacurar, M, Rus, IA: Fixed point theory for cyclic φ-contraction. Nonlinear Anal: Theory Methods Appl. 72(3-4), 1181-1187 (2010). doi:10.1016/j.na.2009.08.002
26. Karapinar, E: Fixed point theory for cyclic weak φ-contraction. Appl Math Lett. 24, 822825 (2011)
27. Shazhad, N, Sadiq Basha, S, Jeyaraj, R: Common best proximity points: global optimal solutions. J Optim Theory Appl. 148(1), 69-78 (2011). doi:10.1007/s10957-010-9745-7
28. Al-Thagafi, MA, Shahzad, N: Convergence and existence results for best proximity points. Nonlinear Anal: Theory Methods Appl. 70(10), 3665-3671 (2009). doi:10.1016/j.na.2008.07.022
29. Vetro, C: Best proximity points: convergence and existence theorems for p-cyclic mappings. Nonlinear Anal: Theory Methods Appl. 73(7), 2283-2291 (2010). doi:10.1016/j.na.2010.06.008