Fixed point results for generalized $\varphi$-contraction on a set with two metrics
Keywords
Set with two metrics, multivalued operator, fixed point, homotopy result, data dependenceAbstract
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 $$ \multline M^T(x,y):=\max \{ \varrho(x,y),D_{\varrho}(x,T(x)),D_{\varrho}(y,T(y)),\\ 2^{-1} [ D_{\varrho}(x,T(y))+D_{\varrho}(y,T(x)) ]\}. \endmultline $$Downloads
Published
2009-06-01
How to Cite
1.
PETRU, Tünde Petra and BORICEANU, Monica. Fixed point results for generalized $\varphi$-contraction on a set with two metrics. Topological Methods in Nonlinear Analysis. Online. 1 June 2009. Vol. 33, no. 2, pp. 315 - 326. [Accessed 29 March 2024].
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