The main aim of this paper is to obtain a unique common tripled fixed point theorem in partial ordered metric space using Caristi type contraction.

In this paper we proved some new Caristi type common fixed point theorems for four maps in a metric space and we gave an applications to Graph theory.

In this paper, we obtained a unique common coupled fixed point theorem using Caristi type contraction in modular metric spaces. Also furnished an example to support our main results.

In this paper we introduced a new notation G – fg –   contraction of Caristi type and a new edge preserving property. With help of these we proved a some coupled fixed point results for four maps endowed with a graph in a complete metric space. Also we gave an application to integral equations.

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