On Kannan-Type Contractive Mappings. (3rd October 2018) - Garai, Hiranmoy; Dey, Lakshmi Kanta; Senapati, Tanusri
Abstract: In this article, we consider Kannan-type contractive self-map T on a metric space ( X, d ) such thatd ( T x, T y ) < 1 2 d ( x, T x ) + d ( y, T y ) for all x ≠ y ∈ X and 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.