PUBLICATIONS DE L'INSTITUT MATHÉMATIQUE (BEOGRAD) (N.S.) Vol. 28(42), pp. 179186 (1980) 

ON FIXED POINT THEOREMS OF MAIA TYPEBogdan RzepeckiOsiedle Bohaterów II Wojny Swiatowej 43/13 61385 Pozna\'n, PolandAbstract: In this note we present some variants of the following result of Maia [10]: Let $X$ be a nonempty 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 $X$. Full text of the article:
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