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Some fixed point results in cone metric spaces for rational contractions. (English) Zbl 1474.54190

Summary: In this paper, we prove the some fixed point theorem in cone metric spaces for rational expression in normal cone setting. Our results generalized the main result of B. K. Dass and S. Gupta [Indian J. Pure Appl. Math. 6, 1455–1458 (1975; Zbl 0371.54074)].

MSC:

54H25 Fixed-point and coincidence theorems (topological aspects)
54E35 Metric spaces, metrizability
54E50 Complete metric spaces
37C25 Fixed points and periodic points of dynamical systems; fixed-point index theory; local dynamics

Citations:

Zbl 0371.54074
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References:

[1] B. Fisher, Common Fixed Points and Constant Mappings Satisfying Rational Inequality, (Math. Sem. Notes (Univ Kobe) (1978). · Zbl 0448.54043
[2] B. Fisher, M.S. Khan, Fixed points, common fixed points and constant mappings, Studia Sci. Math. Hungar. 11 (1978) 467-470. · Zbl 0379.54018
[3] L.G. Huang and X. Zhang, Cone metric spaces and fixed point theorems of contractive mappings, Journal of Mathematical Analysis and Applications, 332 (2) (2007) 1468-1476. · Zbl 1118.54022
[4] S. Rezapour, R. Hamlbarani, Some note on the paper cone metric spaces and fixed point theorems of contractive mappings, J. Math. Anal. Appl. 345 (2008) 719-724. · Zbl 1145.54045
[5] J. O. Olaleru, Some Generalizations of Fixed Point Theorems in Cone Metric Spaces, Fixed Point Theory and Applications, (2009) Article ID 657914. · Zbl 1203.54043
[6] Xiaoyan Sun, Yian Zhao, Guotao Wang, New common fixed point theorems for maps on cone metric spaces, Applied Mathematics Letters 23 (2010) 10331037. · Zbl 1195.54089
[7] Mehdi Asadi, S. Mansour Vaezpour, Vladimir Rakocevic, Billy E. Rhoades, Fixed point theorems for contractive mapping in cone metric spaces, Math. Commun. 16 (2011) 147-155. · Zbl 1217.54038
[8] Mahpeyker OzturkOn, Metin Basarr, Some common fixed point theorems with rational expressions on cone metric spaces over a Banach algebra, Hacet tepe Journal of Mathematics and Statistics, 41 (2) (2012) 211-222. · Zbl 1294.54033
[9] Muhammad arshad, Erdal Karapinar Jamshaid Ahmad, Some Unique Fixed Point Theorems For Rational Contractions In Partially Ordered Metric Spaces, Journal of Inequalities and Applications 2013, 2013:248 doi:10.1186/1029242X-2013-248. · Zbl 1527.54019
[10] D.S. Jaggi, Some unique fixed point theorems, Indian J. Pure Appl. Math. 8 (1977) 223-230. · Zbl 0379.54015
[11] Dass, B.
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