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A general fixed point theorem for four weakly compatible mappings satisfying an implicit relation. (English) Zbl 1089.54022
A theorem improving three known results in fixed point theory is proved. The theorem gives conditions under which four self-mappings of a metric space \(X\) have a (unique) common fixed point. The conditions involve weak compatibility of pairs of mappings (instead of compatibility) and an implicit relation defined by a class of real-valued continuous functions of six real variables (instead of completeness).

MSC:
54H25 Fixed-point and coincidence theorems (topological aspects)
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