Some fixed point generalizations are not real generalizations

Fixed point results for generalized contractive mappings involving altering distance functions on complete quasi-metric spaces and applications

“…However, Haghi et al [8] proved that some generalizations in fixed point theory are not real generalizations. Moreover, Rosa and Vetro [14] established some common fixed point theorems for a large class of α-ψ-ϕ-contractions in generalized metric spaces.…”

Erratum to: Common fixed point theorems for expansion mappings in various spaces

“…Let f and g be weakly compatible (whenever fx (gx, gy) for each x, y ∈ X and q > 1. As an application of axiom of choice, Haghi et al [1] proved a lemma and showed that some coincidence point or common fixed point abstractions in fixed point theory are not real abstractions as they could easily be obtained from the corresponding fixed point theorems. The lemma (below) also provides an interesting criterion for categorization of generalized common fixed point theorem into classes of well known fixed point theorem which are already known in the setting of metric spaces or more general metric spaces (for more details see [1]).…”

Fixed Point and Common Fixed Point Theorems for Cyclic Quasi-Contractions in Metric and Ultrametric Spaces

“…Let X be a nonempty set and Theorem 3.5 can be proved using the analogous ideas of the proofs in Section 2. However, we prove Theorem 3.5 differently by using the following lemma ( [8] . This completes the proof.…”