We extend the celebrated result of W. A. Kirk that a metric space X is complete if and only if every Caristi self-mapping for X has a fixed point, to partial metric spaces.

Abstract. We generalize the notions of fuzzy metric by Kramosil and Michalek, and by George and Veeramani to the quasi-metric setting. We show that every quasi-metric induces a fuzzy quasi-metric and, conversely, every fuzzy quasi-metric space generates a quasi-metrizable topology. Other basic properties are discussed.2000 AMS Classification: 54A40, 54E35, 54E15.

In the present paper, considering a new concept of multivalued almost F-contraction, we give a general class of multivalued weakly Picard operators on complete metric spaces. Also, we give some illustrative examples showing that our results are proper generalizations of some previous theorems.

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