In this paper, using a combination of methods used in [1], [20] and [22] the results from [3, Theorem 1], [14, Theorem 1] and [15, Theorem 1] are improved removing the assumption of continuity, relaxing compatibility to the weak compatibility property and replacing the completeness of the space with a set of four alternative conditions for four functions satisfying an implicit relation. 2000 Mathematics Subject Classification. 54H25
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Valeríu Popa (2024) studied this question.
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