DOI: 10.24193/fpt-ro.2023.2.15

Authors: Mădălina Păcurar

Abstract: Motivated by the existence of cyclic phenomena in which some characteristics are mapped into corresponding ones over more than one phase, we introduce the $-cyclic operators with respect to a covering of a metric space and investigate their behavior. We study the convergence of the Picard iteration to a fixed point of such an operator under a Banach type generalized contraction condition. The obtained results may have interesting practical applications in various research areas.

Key Words and Phrases: Cyclic covering, r-cyclic operator, synchronous r-cyclic contraction, fixed point, Picard operator.

2010 Mathematics Subject Classification: 47H10, 54H25, 03Exx.

Published on-line: June 15th, 2023.

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