Edelstein–Suzuki-type fixed point results in metric and abstract metric spaces

Generalizations of the Edelstein–Suzuki theorem [T. Suzuki, A new type of fixed point theorem in metric spaces, Nonlinear Anal. TMA 71 (2009), 5313–5317], including versions of the Kannan, Chatterjea and Hardy–Rogers-type fixed point results for compact metric spaces, are proved. Also, abstract metric versions of these results are obtained. Examples are presented to distinguish our results from the existing ones.