Title: Strict fixed point problem, stability results and retraction displacement condition for Picard operators Show Chinese title

Title: Picard算子的严格不动点问题、稳定性结果与收缩位移条件

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. Show Chinese abstract

Abstract: 本文的目的是给出严格不动点原理，适用于满足某些 Ćirić 型和 Ćirić-Reich-Rus 型压缩条件的多值算子$T:X\rightarrow P(X)$。 我们感兴趣的是，在什么条件下，多值算子具有唯一的严格不动点，并且进一步当其多值迭代序列$(T^n(x))_{n\in \mathbb{N}}$收敛到这个唯一的严格不动点时。 此外，还建立了某些稳定性性质，例如关于算子扰动的数据依赖性、Ulam-Hyers 稳定性、Reich 和 Zaslavski 意义下的适定性以及严格不动点问题的 Ostrowski 性质。