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Fixed points of multifunctions on regular cone metric spaces. (English) Zbl 1193.47058

In this paper, the authors first prove that every metric space is a regular cone metric space and then they extend a result about Meir-Keeler type contraction mappings on metric spaces to regular cone metric spaces. They also provide an example to show that their result is an extension of Meir-Keeler’s theorem. Some results about fixed points of weakly uniformly strict \(p\)-contraction multifunctions on regular cone metric spaces are established.

MSC:

47H10 Fixed-point theorems
47H04 Set-valued operators
54H25 Fixed-point and coincidence theorems (topological aspects)
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[1] Abbas, M.; Jungck, G., Common fixed point results for noncommuting mappings without continuity in cone metric spaces, J. Math. Anal. Appl., 341, 416-420 (2008) · Zbl 1147.54022
[2] Abbas, M.; Rhoades, B. E., Fixed and periodic point results in cone metric spaces, Appl. Math. Lett., 22, 511-515 (2009) · Zbl 1167.54014
[3] Cardinali, T.; Rubbioni, P., An extension to multifunctions of the Meir-Keeler’s fixed point theorem, Fixed Point Theory, 7, 1, 23-36 (2006) · Zbl 1111.47047
[4] Long-Guang, H.; Xian, Z., Cone metric spaces and fixed point theorems of contractive mappings, J. Math. Anal. Appl., 332, 1468-1476 (2007) · Zbl 1118.54022
[5] Ilic, D.; Rakocevic, V., Common fixed points for maps on cone metric space, J. Math. Anal. Appl., 341, 876-882 (2008) · Zbl 1156.54023
[6] Jachymski, J., Equivalent conditions and the Meir-Keeler type theorems, J. Math. Anal. Appl., 194, 293-303 (1995) · Zbl 0834.54025
[7] Meir, A.; Keeler, E., A theorem on contraction mappings, J. Math. Anal. Appl., 28, 326-329 (1969) · Zbl 0194.44904
[8] Park, S.; Rhoades, B. E., Meir-Keeler type contractive conditions, Math. Japon., 26, 13-20 (1981) · Zbl 0454.54030
[9] Rezapour, Sh.; Hamlbarani, R., Some notes on the paper “Cone metric spaces and fixed point theorems of contractive mappings”, J. Math. Anal. Appl., 345, 719-724 (2008) · Zbl 1145.54045
[10] Rhoades, B. E.; Park, S.; Moon, K. B., On generalizations of the Meir-Keeler type contraction maps, J. Math. Anal. Appl., 146, 482-494 (1990) · Zbl 0711.54028
[11] Vetro, P., Common fixed points in cone metric spaces, Rend. Circ. Mat. Palermo, (2), 56, 3, 464-468 (2007) · Zbl 1196.54086
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