Fixed point uniqueness of generalized (\psi , \varphi)-weak contractions in partially ordered metric spaces under suitable constraints

In this paper, by providing an example, we show that the condition which produced by Radenovi\'{c} and Kadelburg in [Generalized weak contractions in partially ordered metric spaces, Comput. Math. Appl. ۶۰ (۲۰۱۰) pp. ۱۷۷۶-۱۷۸۳] is not sufficient for the uniqueness of the fixed point. Furthermore, a new sufficient condition is introduced for the uniqueness of the fixed point. Some suitable examples are furnished to demonstrate the validity of the hypotheses of our results.

Keywords:

Fixed point , Generalized (\psi , \phi)-Weak Contraction , ordered metric space