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Some new common fixed point theorems under strict contractive conditions. (English) Zbl 1008.54030
Let $(X,d)$ be a metric space and $S,T:X\to X$ two mappings. The authors define a new property for $(S,T)$ which generalizes the concept of noncompatible mappings and give some common fixed point theorems under strict contractive conditions.

54H25Fixed-point and coincidence theorems in topological spaces
47H10Fixed-point theorems for nonlinear operators on topological linear spaces
Full Text: DOI
[1] Jachymski, J.: Common fixed point theorems for some families of maps. Indian J. Pure appl. Math. 25, 925-937 (1994) · Zbl 0811.54034
[2] Jungck, G.; Moon, K. B.; Park, S.; Rhoades, B. E.: On generalization of the Meir--Keeler type contraction maps: corrections. J. math. Anal. appl. 180, 221-222 (1993) · Zbl 0790.54055
[3] Pant, R. P.: Common fixed points of sequences of mappings. Ganita 47, 43-49 (1996) · Zbl 0892.54028
[4] Jungck, G.: Compatible mappings and common fixed points. Internat. J. Math. math. Sci. 9, 771-779 (1986) · Zbl 0613.54029
[5] Pant, R. P.: R-weak commutativity and common fixed points. Soochow J. Math. 25, 37-42 (1999) · Zbl 0918.54038
[6] Pant, R. P.: Common fixed points of contractive maps. J. math. Anal. appl. 226, 251-258 (1998) · Zbl 0916.54027
[7] Sessa, S.: On a weak commutativity condition of mappings in fixed point considerations. Publ. inst. Math. (Beograd) 32, 149-153 (1982) · Zbl 0523.54030
[8] Caristi, J.: Fixed point theorems for mapping satisfying inwardness conditions. Trans. amer. Math. soc. 215, 241-251 (1976) · Zbl 0305.47029