| Abstrakt: |
In the present paper, we introduce a new type of mappings in metric spaces, which are three point analogues of the well-known Kannan type mappings, and refer to them as generalized Kannan type mappings. It is shown that, in general, Kannan type mappings and generalized Kannan type mappings are independent of each other besides being discontinuous in the domain but continuous at fixed points. A fixed-point theorem for generalized Kannan type mappings is proved. It is shown that additional conditions of asymptotic regularity and continuity of the mapping pave the way to extend the fixed-point theorem for generalized Kannan type mappings. Lastly, we derive two other fixed-point theorems for generalized Kannan type mappings in metric spaces, which are not necessarily complete. Our assertions are validated by several nontrivial examples. [ABSTRACT FROM AUTHOR] |
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