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Zbl 1213.54066
Imdad, M.; Soliman, Ahmed H.
Some common fixed point theorems for a pair of tangential mappings in symmetric spaces.
(English)
[J] Appl. Math. Lett. 23, No. 4, 351-355 (2010). ISSN 0893-9659

In this note the authors consider two common fixed point theorems proved by {\it R. P. Pant} [J. Math. Anal. Appl. 240, No.~1, 280--283 (1999; Zbl 0933.54031)] and by {\it K. P. R. Sastry} and {\it J. S. R. Krishma Murthy} [ibid. 250, No.~2, 731--734 (2000; Zbl 0977.54037)] and prove their analogues in a symmetric space setting. Let us recall that a notion of a symmetric on a non-empty set was introduced by Menger in 1928 and it denotes a function $d:X\times X\to [0,+\infty)$ such that $d(y,x)=d(x,y)$ and $d(x,x)=0$ (for all $x,\ y\in X$ ).
[Dariusz Bugajewski (Baltimore)]
MSC 2000:
*54H25 Fixed-point theorems in topological spaces
54E25 Semimetric spaces

Keywords: compatible mappings; non-compatible mappings; partially commuting mappings; $R$-weakly commuting mappings; tangential mappings; Lipschitz mapping; coincidence point; fixed point

Citations: Zbl 0933.54031; Zbl 0977.54037

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