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Fixed point theory for cyclic Berinde operators. (English) Zbl 1237.54057
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.
MSC:
54H25Fixed-point and coincidence theorems in topological spaces
54E40Special maps on metric spaces