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Zbl 1155.54027
Pant, Vyomesh
Common fixed points under Lipschitz type condition. (English)
[J] Bull. Korean Math. Soc. 45, No. 3, 467-475 (2008). ISSN 1015-8634

This paper contains five theorems. These results include the following: Let $f$ and $g$ be noncompatible pointwise $R$-weakly commuting self-mappings of a metric space $(X,d)$ satisfying\par (i) $\overline{fX}\subset gX$, where $\overline{fX}$ denotes the closure of range of $f$,\par (ii) $d(fx,fy)\le k$, $d(gx,gy)$, $k\ge 0$, and\par (iii) $d(fx,f^2x)< \max\{d(gx, gfz)$, $d(g^2x, gfx)$, $d(fx,gx)$, $d(f^2x, gfx)$, $d(fx,gfx)$, $d(gx,f^2x)\}$,\par whenever $fx\ne f^2x$. Then $f$ and $g$ have a common fixed point.
[K. Chandrasekhara Rao (Kumbakonam)]

MSC 2000:: *54H25 Fixed-point theorems in topological spaces

Keywords: Lipschitz type mapping pairs; contractive conditions; property (E.A.) noncompatible mappings

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