DOI: 10.24193/fpt-ro.2025.1.16

Authors: Mădălina Păcurar

Abstract: Cyclic (1-cyclic) operators have been studied in a long list of papers over the last decade. r-cyclic operators were introduced recently [Păcurar, M., Synchronous r-cyclic contractions on metric spaces, Fixed Point Theory, 24 (2023), No. 2, 683-700] and show interesting properties. In the present paper we introduce asynchronous r-cyclic contractions condition and study the conditions under which they are Picard operators. Their behavior is compared to the one of the synchronous r-cyclic contractions. Besides generalizing known results, our approach opens a research direction with some potential, both theoretical and practical.

Key Words and Phrases: r-cyclic covering, iterative method, fixed point, Picard operator, seasonal variability.

2010 Mathematics Subject Classification: 47H10, 54H25.

Published on-line: February 1st, 2025.

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