A generalization Caristi Kirk's theorem for common fixed points on \(G\)-metric spaces (Q2798825)

The authors obtain coincidence and fixed point theorems for self mappings satisfying a Caristi-type contractive condition in a \(G\)-metric space in the sense of \textit{Z. Mustafa} and \textit{B. Sims} [J. Nonlinear Convex Anal. 7, No. 2, 289--297 (2006; Zbl 1111.54025)].NEWLINENEWLINENote that Example 2.6 that is designated to illustrate the main result of the paper (Theorem 2.3) is covered by a simpler result, i.e., by the \textit{G. Jungck}'s common fixed theorem in usual metric spaces [Amer. Math. Monthly 83, 261--263 (1976; Zbl 0416.54025]), since \(T\) and \(S\) are continuous, commute and NEWLINE\[NEWLINE\left |\frac{3}{8}x-\frac{3}{8}y\right |\leq \frac{3}{4}\left |\frac{1}{2}x-\frac{1}{2}y\right |,\forall x,y\in [0,+\infty). NEWLINE\]