An Implicit Function Implies Several Contraction Conditions

Abstract

In this paper, we define a new implicit function which includes a majority of contractions of the existing literature of metric fixed point theory and then utilize the same to prove a general common fixed point theorem for two pairs of weakly compatible mappings satisfying the common property $(E.A)$. In the process, a host of previously known results are improved and generalized. Some related results are derived besides furnishing illustrative examples. 2000 Mathematics Subject Classification. 47H10, 54H25

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