In this paper, we obtain some fixed point theorems for fuzzy mappings in a left K-sequentially complete quasi-pseudo-metric space and in a right K-sequentially complete quasi-pseudo-metric space, respectively. Our analysis is based on the fact that fuzzy fixed point results can be obtained from the fixed point theorem of multivalued mappings with closed values. It is observed that there are many situations in which the mappings are not contractive on the whole space but they may be contractive on its subsets. We feel that this feature of finding the fuzzy fixed points via closed balls was overlooked, and our paper will re-open the research activity into this area.