We formulate a common fixed point theorem for four non-self mappings in convex partial metric spaces. The result extends a fixed point theorem by Gajić and Rakočević (2007) proved for two non-self mappings in metric spaces with a Takahashi convex structure. We also provide an illustrative example on the use of the theorem.
The notions of compatible mappings play a crucial role in metrical fixed point theory. Partial metric spaces are a generalization of the notion of a metric space in the sense that distance of a point from itself is not necessarily zero. In this paper, we prove coincidence and fixed point theorems for a pair of single-valued and multi-valued weak compatible mappings on a complete partial metric space. Our main results generalize, in particular, the results of Kaneko and Sessa (1989), Pathak (1995)...
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