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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.

##### MSC:
 54H25 Fixed-point and coincidence theorems (topological aspects) 47H10 Fixed-point theorems
##### Keywords:
fixed point; weakly compatible mapping
Full Text:
##### References:
 [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
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