FIXED POINT THEOREMS FOR ONE AND TWO SELF-MAPS ON A G-METRIC SPACE

Abstract

The proof of a recent result of Vats et al is presented, by employing the infimum property of nonegative real numbers.  Then the unique fixed point is shown to be the G-limit of all the orbits of the form x, fx, ..., f ⁿx, ..., x ∈ X.  That is, the unique fixed point is a G-contractive fixed point.  Further, a fixed point for a pair of self-maps is obtained as another application of the infimum property.