In this paper, we revisit the renowned fixed point theorems of Ćirić and Caristi. We propose some new fixed point theorems in a metric space with partial order. To make our results effective, several examples are presented.
In this paper, we extend Caristi’s fixed point theorem in metric spaces to probabilistic metric spaces, and also, we prove some common fixed point theorems for a pair of mappings satisfying a system of Caristi-type contractions in the setting of a Menger space. Two examples are given to support the main results. Furthermore, we have functional equations as an application for the main theorem.
In this paper, we present some new best proximity point theorems for three operators acting in Banach algebras. An application is given to show the usefulness and the applicability of the obtained results.
The aim of this paper is to discuss Penot's problem on a generalization of Caristi's fixed point theorem and prove new positive results. We present some new existence theorems of fixed point problem for set-valued mappings in ordered metric spaces.
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