Summary: Inspired by the considerations in [W. A. Kirk
, P. S. Srinivasan
and P. Veeramani
, Fixed Point Theory 4, No. 1, 79–89 (2003; Zbl 1052.54032
)], which were further discussed in [I. A. Rus
, “Cyclic representations and fixed points”, Ann. T. Popoviciu Seminar Funct. Eq. Approx. Convexity 3, 171–178 (2005)], we establish the existence and uniqueness of the fixed point for cyclic strict Berinde operators. Following [I. A. Rus
, Fixed Point Theory 9, No. 2, 541–559 (2008; Zbl 1172.54030
)], we build a so-called theory of the main result, referring concepts and phenomena like Picard operators, data dependence, limit shadowing, well-posedness of the fixed point problem. A Maia type result for cyclic strict Berinde operators is also given.