DOI: 10.24193/fpt-ro.2023.2.05

Authors: Vasile Berinde, Adrian Petrușel and Ioan A. Rus

Abstract: In this paper we present some suggestions for unifying the terminology of the mappings appearing in fixed point iterative methods for the case when the setting is a metric space. We consider the following concepts: contraction type mapping, contractive type mapping and nonexpansive type mapping, for which some problems are formulated.

Key Words and Phrases: Metric spaces, contraction mapping, contractive mapping, nonexpansive mapping, quasicontraction, quasicontractive, quasinonexpansive, cyclic contraction, cyclic contractive mapping, cyclic nonexpansive mapping, graphic contraction, graphic contractive mapping, graphic nonexpansive mapping, Caristi mapping, Caristi-Browder mapping, Caristi-Kirk mapping, weakly Picard mapping, Picard mapping, well-posedness of fixed point problem, Ostrowski property, data dependence, open problem.

2010 Mathematics Subject Classification: 47H10, 47H09, 54H25, 65J15.

Published on-line: June 15th, 2023.

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