Fixed point results for generalized $\varphi$-contraction on a set with two metrics
Słowa kluczowe
Set with two metrics, multivalued operator, fixed point, homotopy result, data dependenceAbstrakt
The aim of this paper is to present fixed point theorems for multivalued operators $ T\colon X \to P(X)$, on a nonempty set $X$ with two metrics $d$ and $\varrho$, satisfying the following generalized $\varphi$-contraction condition: $$ H_{\varrho}(T(x),T(y))\leq \varphi(M^T(x,y)),\quad \text{for every } x,y \in X, $$ where $$ \multline M^T(x,y):=\max \{ \varrho(x,y),D_{\varrho}(x,T(x)),D_{\varrho}(y,T(y)),\\ 2^{-1} [ D_{\varrho}(x,T(y))+D_{\varrho}(y,T(x)) ]\}. \endmultline $$Pobrania
Opublikowane
2009-06-01
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PETRU, Tünde Petra & BORICEANU, Monica. Fixed point results for generalized $\varphi$-contraction on a set with two metrics. Topological Methods in Nonlinear Analysis [online]. 1 czerwiec 2009, T. 33, nr 2, s. 315–326. [udostępniono 22.7.2024].
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