SOME REMARKS ON THE PAPER “SOME FIXED POINT GENERALIZATIONS ARE NOT REAL GENERALIZATIONS”

In this short paper we show that the results obtained by using the axiom of choice in [r.h. haghi, sh. rezapour and s. naseer: some fixed point generalizations are not real generalizations, nonlinear anal., 77(2011), 1799-1803], [n. hussain, a. latif andm.h. shah: coupled and tripled coincidence point results without compatibility, fixed point theory appl., 2012, 2012:77] and [b.k. bisht, m. jain and s. kumar: erratum to: common fixed point theorems for expansion mappings in various spaces, actamath. hungar., 146(2015), no. 1, 261-264] are weaker than the ones obtained without axiomof choice. furthermore, we claim that all known results with two self-maps f, g : x → x satisfying f(x) ⊆ g(x) do be genuine generalizations of the results with one self-map f : x → x.