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Let  be a boundedly compact metric space. Let T be a Kannan type contractive selfmap of X. That is, T fulfills the following property:

                   for all                        (K-S)

The condition (K-S) is not sufficient to ensure fixed point for T. The aim of this paper is to investigate necessary and sufficient conditions making T be a Picard operator. This work is motivated by some recent papers published by Górnicki, Garai, Senapati and Dey. Our work has relationships with other recent aricles on Kannan type contractive selfmaps. We propose here some new results and complements. Also, we provide examples to support our investigations. 

metric space, boundedly compact set, T-orbitally compact space, Kannan type mapping, orbitally continuous mappings.