DOI: 10.24193/fpt-ro.2020.1.11

Authors: T. Domínguez Benavides, P. Lorenzo Ramírez, M. Rahimi and A. Sadeghi Hafshejani

Abstract: This paper focus on the class of multivalued iterated contractions, mappings which are contractive throughout the orbits. We show that the proof of Nadler's theorem still holds for these mappings whenever they satisfy a rather weak type of continuity, which gives us a new fixed point theorem. We show several types of mappings that properly contain Suzuki (C)-type generalized contraction mappings and for which our fixed point results apply. We conclude the paper showing some further examples of iterated contraction mappings which are, respectively, the mappings satisfying condition (B) and an extension to the multivalued case of mean iterated contractions and we also obtain fixed point results for these classes of mappings.

Key Words and Phrases: Fixed point, multivalued mappings, generalized contraction mappings, metric spaces.

2010 Mathematics Subject Classification: 47H04, 47H09, 47H10.

Published on-line: February 1st, 2020.

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