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Let  be a complete metric space. Let f be a given selfmap of X. A selfmap T of X is said to be a Ćirić strong almost contraction with respect to f if there exist constants  and  such that the following condition is fulfilled:

                                                                    (C-B)

for all  where

This concept extends and unifies many concepts already known in the literature like the Ćirić strong almost contraction, almost (or weak) contractions introduced by Berinde or the condition (B)’ of Babu et al. [4] or its generalization due to Abbas et al. [2].

In this paper, we investigate coincidence points of a pair  satisfying the condition (C-B) and look for conditions ensuring the existence of common fixed points. The results obtained in this line provide generalizations of several published results. We provide examples supporting our results. We end this work by discussing a problem concerining the Ćirić almost contractions introduced by Berinde in 2009.

complete metric space, fixed point, sequences of mappings.