PUBLICATIONS DE L'INSTITUT MATHÉMATIQUE (BEOGRAD) (N.S.)
Vol. 28(42), pp. 179--186 (1980)
ON FIXED POINT THEOREMS OF MAIA TYPE
Bogdan RzepeckiOsiedle Bohaterów II Wojny Swiatowej 43/13 61385 Pozna\'n, Poland
Abstract: In this note we present some variants of the following result of Maia : 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 $X$.
Full text of the article:
Electronic fulltext finalized on: 3 Nov 2001. This page was last modified: 22 Aug 2002.
© 2001 Mathematical Institute of the Serbian Academy of Science and Arts