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A common fixed point theorem for weakly compatible mappings in symmetric spaces satisfying a contractive condition of integral type. (English) Zbl 1111.47046
The author considers weak compatible selfmaps of a symmetric space and proves a common fixed point theorem by using a contractive condition of integral type, generalizing results of {\it M. Aamri} and {\it D. El Moutawakil} [J. Math. Anal. Appl. 270, No. 1, 181--188 (2002; Zbl 1008.54030); Appl. Math. E-Notes 3, 156--162 (2003; Zbl 1056.47036)].

47H10Fixed-point theorems for nonlinear operators on topological linear spaces
54H25Fixed-point and coincidence theorems in topological spaces
54E25Semimetric spaces
47H09Mappings defined by “shrinking” properties
Full Text: DOI
[1] Aamri, M.; El Moutawakil, D.: Common fixed points under contractive conditions in symmetric spaces. Appl. math. E-notes 3, 156-162 (2003) · Zbl 1056.47036
[2] Aamri, M.; El Moutawakil, D.: Some new common fixed point theorems under strict contractive conditions. J. math. Anal. appl. 270, 181-188 (2002) · Zbl 1008.54030
[3] Jungck, G.: Compatible mappings and common fixed points. Internat. J. Math. math. Sci. 9, 771-779 (1986) · Zbl 0613.54029
[4] Jungck, G.; Rhoades, B. E.: Fixed points for set valued functions without continuity. Indian J. Pure. appl. Math. 29, No. 3, 227-238 (1998) · Zbl 0904.54034
[5] Pant, R. P.: Common fixed points of contractive maps. J. math. Anal. appl. 226, 251-258 (1998) · Zbl 0916.54027
[6] Pant, R. P.: Common fixed points of sequences of mappings. Ganita 47, 43-49 (1996) · Zbl 0892.54028
[7] Hicks, T. L.; Rhoades, B. E.: Fixed point theory in symmetric spaces with applications to probabilistic spaces. Nonlinear anal. 36, 331-344 (1999) · Zbl 0947.54022
[8] Rhoades, B. E.: Two fixed point theorems for mappings satisfying a general contractive condition of integral type. Internat. J. Math. math. Sci. 63, 4007-4013 (2003) · Zbl 1052.47052
[9] Sessa, S.: On a weak commutativity condition of mappings in fixed point considerations. Publ. inst. Math. (Beograd) 32, No. 46, 149-153 (1982) · Zbl 0523.54030
[10] Wilson, W. A.: On semi-metric spaces. Amer. J. Math. 53, 361-373 (1931) · Zbl 0001.22804