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The purpose of this paper is to obtain best proximity point theorems for a weakly contractive mapping and a weakly Kannan mapping in partial metric spaces. In this paper, the P-operator technique, which changes a non-self mapping to a self mapping, provides a key method. Many recent results in this area have been improved. MSC: 47H05, 47H09, 47H10.
Abkar and Gabeleh in (J. Optim. Theory. Appl. doi: 10.1007/s10957-011-9818-2 ) proved some theorems which ensure the existence and convergence of fixed points, as well as best proximity points for cyclic mappings in ordered metric spaces. In this paper we extend these results to generalized cyclic contractions and obtain some new results on the existence and convergence of fixed points for weakly...
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