Browsing by Author "Johnson, Kessy"

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    Common Fixed Points for Weakly Compatible Mappings in Partial Metric Spaces
    (Busan International Nonlinear Analysis Academy, 2018-03-01) Johnson, Kessy; Santosh, Kumar; Grayson, Kakiko
    In many situations the arising mappings need not be self-mappings. It is well known that metrically convex metric spaces are desirable for the study of fixed points of non-self mappings. Partial metric spaces are generalization of the notion of a metric space that allows non-zero self distance. In this paper, we present a common fixed point theorem for weakly compatible mappings on complete metrically convex partial metric spaces. Our main result generalizes a common metric fixed point theorem due to ´Ciri´c and Ume, which is an extension of a metric fixed point theorem due to Rhoades, to partial metric spaces.
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    FIXED POINTS FOR HYBRID PAIR OF COMPATIBLE MAPPINGS IN PARTIAL METRIC SPACES
    (Scik.org, 2017) Johnson, Kessy; Kumar, Santosh; Kakiko, Grayson
    In this paper coincidence and fixed point theorems for a pair of single-valued and multi-valued compatible mappings on complete partial metric spaces are presented. The notion of compatible mappings for a pair of single-valued and multi-valued mappings proved to be very useful as the existing metric fixed point theory contains numerous fixed point results for pair(s) of mappings established under compatibility condition and its generalizations. Partial metric spaces are one of generalizations of the notion of a metric space that allows non-zero self distance. The existing metric fixed point theory approaches, are adapted to establish the results. The main result generalizes, in particular, a fixed point theorem due to Kaneko and Sessa for hybrid pair of compatible mappings. An illustrative example is also provided.