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.