FIXED POINTS FOR MONOTONE ITERATIVELY LOCAL CONTRACTIONS

Mihai Turinici (1)

1 Faculty of Mathematics, University Al. I. Cuza, Iasi, Romania

Let the quasi-ordered metric space $(X,d,\le)$ and the increasing self-mapping $T$ of $X$ be such that: for each $x\in X$ with $x\le Tx$, there exists a rank $n(x)\in N$ and an increasing function $f(x):R_+^{2n(x)+1} \to R_+$ with $d(T^{n(x)}x,T^{n(x)}y)\le f(x)(d(x,Tx),...,d(x,T^{n(x)}x);d(x,y),...,d(x,T^{n(x)}y))$, for all $y\in X$, $x\le y\le Ty$; then, under some additional assumptions involving these elements, $T$ has at least one fixed point in $X$. A number of related contributions in this direction due to Sehgal, Guseman and Matkowski are obtained as corollaries.

Domaines: Topologie générale [math.GN]

Mihai Turinici. FIXED POINTS FOR MONOTONE ITERATIVELY LOCAL CONTRACTIONS. Demonstratio Mathematica, 1986, XIX (1), pp.171-180. ⟨hal-01188275⟩