Some Partial Metric Spaces of Sequences and Functions

In this paper, we investigate some notions of the classical sets of sequences and functions by using the partial metrics with respect to the partial ordering. Also, we examine the completeness of these spaces and obtain the alpha-, beta- and gamma-duals of some of these. We investigate the relationships between these sets and their classical forms and give some properties including definitions, propositions and various kinds of partial metric spaces. Finally, we show that each of the sets forms a vector space on the real field and present some results on the completeness of these partial metric spaces.