Geodesic
On Fixed Point Theorems of Maia Type
Publications de l'Institut Mathématique, _N_S_28 (1980) no. 42, p. 179 
Bogdan Rzepecki. On Fixed Point Theorems of Maia Type. Publications de l'Institut Mathématique, _N_S_28 (1980) no. 42, p. 179 . http://geodesic.mathdoc.fr/item/PIM_1980_N_S_28_42_a22/
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Voir la notice de l'article provenant de la source eLibrary of Mathematical Institute of the Serbian Academy of Sciences and Arts

In this note we present some variants of the following result of Maia [10]: Let $X$ be a non-empty set endowed in with two metrics $\rho$, $\sigma$, and let $f$ be a mapping of $X$ into itself. Suppose that $\rho(x,y)\leq\sigma(x,y)$ in $X$, $X$ is a complete space and $f$ is continuous with respect to $\rho$, and $\sigma(fx,fy)\leq k\cdot\sigma(x,y)$ for all $x$, $y$ in $X$, where $0 \leq k 1$. Then, $f$ has a unique fixed point in $X$.