## Common fixed points under Lipschitz type condition.(English)Zbl 1155.54027

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
(i) $$\overline{fX}\subset gX$$, where $$\overline{fX}$$ denotes the closure of range of $$f$$,
(ii) $$d(fx,fy)\leq k$$, $$d(gx,gy)$$, $$k\geq 0$$, and
(iii) $$d(fx,f^2x)< \max\{d(gx, gfz)$$, $$d(g^2x, gfx)$$, $$d(fx,gx)$$, $$d(f^2x, gfx)$$, $$d(fx,gfx)$$, $$d(gx,f^2x)\}$$,
whenever $$fx\neq f^2x$$. Then $$f$$ and $$g$$ have a common fixed point.

### MSC:

 54H25 Fixed-point and coincidence theorems (topological aspects)
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