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Fixed point theorem for cyclic Chatterjea type contractions. (English) Zbl 1251.54049

Summary: We introduce the notion of cyclic weakly Chatterjea type contraction and generalized cyclic weakly Chatterjea type contraction in metric spaces. We discussed the existence of fixed point theorems of (generalized) cyclic weakly Chatterjea type contraction mappings in the context of complete metric spaces. Our main theorems extend and improve some existing fixed point theorems.

MSC:

54H25 Fixed-point and coincidence theorems (topological aspects)
47H10 Fixed-point theorems
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[1] H. K. Nashine, “New fixed point theorems for mappings satisfying generalized weakly contractive condition with weaker control functions,” Annales Polonici Mathematici, vol. 104, pp. 109-119, 2012. · Zbl 1278.54040 · doi:10.4064/ap104-2-1
[2] E. Karapınar, “Weak \varphi -contraction on partial metric spaces and existence of fixed points in partially ordered sets,” Mathematica Aeterna, vol. 1, no. 4, pp. 237-244, 2011.
[3] S. K. Chatterjea, “Fixed-point theorems,” Comptes Rendus de l’Académie Bulgare des Sciences, vol. 25, pp. 727-730, 1972. · Zbl 0274.54033
[4] B. S. Choudhury, “Unique fixed point theorem for weak C-contractive mappings,” Kathmandu University Journal of Science, Engineering and Technology, vol. 5, no. 1, pp. 6-13, 2009.
[5] W. A. Kirk, P. S. Srinivasan, and P. Veeramani, “Fixed points for mappings satisfying cyclical contractive conditions,” Fixed Point Theory, vol. 4, no. 1, pp. 79-89, 2003. · Zbl 1052.54032
[6] C.-M. Chen, “Fixed point theory for the cyclic weaker Meir-Keeler function in complete metric spaces,” Fixed Point Theory and Applications, vol. 2012, article 17, 2012. · Zbl 1273.54046 · doi:10.1186/1687-1812-2012-17
[7] L. Cirić, N. Cakić, M. Rajović, and J. S. Ume, “Monotone generalized nonlinear contractions in partially ordered metric spaces,” Fixed Point Theory and Applications, Article ID 131294, 11 pages, 2008. · Zbl 1158.54019 · doi:10.1155/2008/131294
[8] M. Derafshpour, S. Rezapour, and N. Shahzad, “On the existence of best proximity points of cyclic contractions,” Advances in Dynamical Systems and Applications, vol. 6, no. 1, pp. 33-40, 2011. · Zbl 1227.54046
[9] J. Jachymski, “Equivalent conditions for generalized contractions on (ordered) metric spaces,” Nonlinear Analysis. Theory, Methods and Applications A, vol. 74, no. 3, pp. 768-774, 2011. · Zbl 1201.54034 · doi:10.1016/j.na.2010.09.025
[10] E. Karapınar, “Fixed point theory for cyclic weak \varphi -contraction,” Applied Mathematics Letters, vol. 24, no. 6, pp. 822-825, 2011. · Zbl 1256.54073 · doi:10.1016/j.aml.2010.12.016
[11] E. Karapınar, I. M. Erhan, and A. Y. Ulus, “Fixed point theorem for cyclic maps on partial metric spaces,” Applied Mathematics and Information Sciences, vol. 6, no. 1, pp. 239-244, 2012.
[12] E. Karapınar and K. Sadarangani, “Corrigendum to “fixed point theory for cyclic weak \varphi -contraction” [Appl. Math. Lett. 24 (6) (2011) 822-825],” vol. 25, no. 10, pp. 1582-1584, 2012. · Zbl 1256.54073
[13] E. Karapınar, “Fixed point theory for cyclic (\varphi -\varphi )-contractions,” Applied Mathematics Letters, vol. 24, no. 6, pp. 822-825, 2011. · Zbl 1256.54073 · doi:10.1016/j.aml.2010.12.016
[14] S. Karpagam and S. Agrawal, “Best proximity point theorems for cyclic orbital MeirKeeler contraction maps,” Nonlinear Analysis, Theory, Methods and Applications, vol. 74, no. 4, pp. 1040-1046, 2011. · Zbl 1206.54047 · doi:10.1016/j.na.2010.07.026
[15] G. S. R. Kosuru and P. Veeramani, “Cyclic contractions and best proximity pair theorems,” 2011, http://128.84.158.119/abs/1012.1434v2. · Zbl 1237.54052
[16] K. Neammanee and A. Kaewkhao, “Fixed points and best proximity points for multi-valued mapping satisfying cyclical condition,” International Journal of Mathematical Sciences and Applications, vol. 1, no. 1, atricle 9, 2011. · Zbl 1266.47078
[17] M. P\uacurar and I. A. Rus, “Fixed point theory for cyclic \varphi -contractions,” Nonlinear Analysis. Theory, Methods and Applications A, vol. 72, no. 3-4, pp. 2683-2693, 2010.
[18] M. A. Petric, “Best proximity point theorems for weak cyclic Kannan contractions,” Filomat, vol. 25, no. 145, 154 pages, 2011. · Zbl 1257.47061
[19] I. A. Rus, “Cyclic representations and fixed points,” Annals of the Tiberiu Popoviciu Seminar of Functional Equations, Approximation and Convexity, vol. 3, pp. 171-178, 2005.
[20] S. Banach, “Sur les operations dans les ensembles abstraits et leur application aux equations integerales,” Fundamenta Mathematicae, vol. 3, pp. 133-181, 1922. · JFM 48.0201.01
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