Let $X$ be a non-empty set. We say that an element $x\in X$ is a $\varphi$-fixed point of $T$, where $\varphi: X\to [0,\infty)$ and $T: X\to X$, if $x$ is a fixed point of $T$ and $\varphi(x)=0$. In this paper, we establish some existence results of $\varphi$-fixed points for various classes of operators in the case, where $X$ is endowed with a metric $d$. The obtained results are used to deduce some fixed point theorems in the case where $X$ is endowed with a partial metric $p$.

Jleli, M., Samet, B., Vetro, C. (2014). Fixed point theory in partial metric spaces via $\varphi$-fixed point's concept in metric spaces. JOURNAL OF INEQUALITIES AND APPLICATIONS, 2014, 1-9 [10.1186/1029-242X-2014-426].

### Fixed point theory in partial metric spaces via $\varphi$-fixed point's concept in metric spaces

#### Abstract

Let $X$ be a non-empty set. We say that an element $x\in X$ is a $\varphi$-fixed point of $T$, where $\varphi: X\to [0,\infty)$ and $T: X\to X$, if $x$ is a fixed point of $T$ and $\varphi(x)=0$. In this paper, we establish some existence results of $\varphi$-fixed points for various classes of operators in the case, where $X$ is endowed with a metric $d$. The obtained results are used to deduce some fixed point theorems in the case where $X$ is endowed with a partial metric $p$.
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2014
Settore MAT/05 - Analisi Matematica
Jleli, M., Samet, B., Vetro, C. (2014). Fixed point theory in partial metric spaces via $\varphi$-fixed point's concept in metric spaces. JOURNAL OF INEQUALITIES AND APPLICATIONS, 2014, 1-9 [10.1186/1029-242X-2014-426].
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/10447/103238