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Zbl 1237.54057
Păcurar, Mădălina
Fixed point theory for cyclic Berinde operators. (English)
[J] Fixed Point Theory 12, No. 2, 419-428 (2011). ISSN 1583-5022

Summary: Inspired by the considerations in [{\it W. A. Kirk}, {\it P. S. Srinivasan} and {\it P. Veeramani}, Fixed Point Theory 4, No.~1, 79--89 (2003; Zbl 1052.54032)], which were further discussed in [{\it 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 [{\it 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 2000:: *54H25 Fixed-point theorems in topological spaces
54E40 Special maps on metric spaces

Keywords: cyclic almost contraction; cyclic Berinde operator; Picard operator; data dependence; well-posedness of a fixed point problem; limit shadowing

Citations: Zbl 1052.54032; Zbl 1172.54030

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