Abstract
In this article, we consider Kannan-type contractive self-map T on a metric space (X, d) such thatand establish some new fixed point results without taking the compactness of X and also relaxing the continuity of T. Further, we anticipate a result ensuring the completeness of the space X via fixed point property of this map. Finally, we give an affirmative answer to the open question posed by J. Górnicki [Fixed point theorems for Kannan-type mappings, J. Fixed Point Theory Appl. 2017]. Apart from these, our manuscript consists of several nontrivial examples which signify the motivation of our investigations.
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