We extend the result of Kirk-Saliga and we generalize Alfuraidan and Khamsi theorem for reflexive graphs. As a consequence, we obtain the ordered version of Caristi's fixed point theorem. Some concrete examples are given to support the obtained results.

The purpose of this paper is to establish Fisher fixed point theorem for two single mappings in the setting of partially ordered generalized metric spaces.

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In this paper, by using the idea of combining fixed point theory and graph theory, we shall introduce the concept of G-Kannan contraction in a generalized metric space introduced recently by Jleli and Samet, endowed with graph. In this setting, we investigate the existence and uniqueness of the fixed point for mappings satisfying such contraction. This work unifies and generalizes various known comparable results in the literature.

We discuss Fisher’s fixed point theorem for mappings defined on a generalized metric space endowed with a graph. This work should be seen as a generalization of the classical Fisher fixed point theorem. It extends some recent works on the enlargement of Banach Contraction Principle to generalized metric spaces with graph. An example is given to illustrate our result.