arXiv subjects

Cristina Gheorghe

Publications and source records attributed to Cristina Gheorghe.

3 recordsLinked to original sources

arXiv2025

Admissible perturbations of a multivalued Picard operator: Ćirić contraction condition; fixed point and stability results

This paper studies strict fixed point and stability results for multivalued operators which does not satisfy a Ćirić type contraction condition, but their admissible perturbation does. We focus on the conditions imposed on the admissible perturbation $T_G$ of a Picard operator $T:X\rightarrow P(X)$ such that the strict fixed point and stability results still hold for T. The results obtained are reformulated in terms of admissible perturbations in the sense of Takahashi and illustrated with some examples.

math.FA↗

arXiv2025

Stratified equatorial flows in cylindrical coordinates with surface tension

This paper considers a mathematical model of steady flows of an inviscid and incompressible fluid moving in the azimuthal direction. The water density varies with depth and the waves are propagating under the force of gravity, over a flat bed and with a free surface, on which acts a force of surface tension. Our solution pertains to large scale equatorial dynamics of a fluid with free surface expressed in cylindrical coordinates. We also prove a regularity result for the free surface.

math.AP↗

arXiv2025

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

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 Ćiri\' c and of Ćiri\' 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.

math.FA↗