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By using the partial ordering method, a more general type of Ekeland's variational principle and Caristi's coincidence theorem for set-valued mappings in probabilistic metric spaces are given in this paper. In addition, we give also a directly simple proof of the equivalence between theses theorems in probabilistic metric spaces.
In this paper several fixed point theorems for a class of mappings defined on a complete G-metric space are proved. In the same time we show that if the G-metric space (X, G) is symmetric then the existence and uniqueness of these fixed point results follows from the Hardy-Rogers theorem in the induced usual metric space (X, d G). We also prove fixed point results for mapping on a G-metric space (X, G) by using the Hardy-Rogers theorem where (X, G) need not be symmetric.
