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arXiv · 2503.00207

Strict fixed point problem, stability results and retraction displacement condition for Picard operators

Cristina Gheorghe·Adrian Petruşel
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Abstract

The aim of this paper is to give strict fixed point principles for multivalued operators $T:X\rightarrow P(X)$ satisfying some contraction conditions of \'Ciri\' c and of \'Ciri\' c-Reich-Rus type. We are interested, under which conditions, the multi-valued operator has a unique strict fixed point and, additionally, when the sequence of its multi-valued iterates $(T^n(x))_{n\in \mathbb{N}}$ converges to this unique strict fixed point. Moreover, some stability properties, such as data dependence on operator perturbation, Ulam-Hyers stability, well-posedness in the sense of Reich and Zaslavski and Ostrowski property of the strict fixed point problem are established.

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Cristina Gheorghe, Adrian Petruşel. 2025-02-28. Strict fixed point problem, stability results and retraction displacement condition for Picard operators. https://arxiv.org/abs/2503.00207

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