On stable fixed points under several kinds of strong perturbations

Volume 12, Issue 11, pp 699--710 http://dx.doi.org/10.22436/jnsa.012.11.01

Publication Date: June 15, 2019 Submission Date: April 26, 2019 Revision Date: May 14, 2019 Accteptance Date: May 28, 2019

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Authors

Qi-Qing Song - College of Science, Guilin University of Technology, Guilin 541004, China. Ping Luo - College of Science, Guilin University of Technology, Guilin 541004, China.

Abstract

This gives new results on stable fixed points related to several kinds of strong perturbations in references. It is shown that a strong stable set of fixed points has a robust stable property. For a robust stable fixed point set of a correspondence, in its neighborhood, there is a strong stable set for any small perturbation of the correspondence. There exists a robust stable set for a correspondence, if there is at least one fixed point for the correspondence. These generalize the corresponding results in recent references and give an application in the existence of strong stable economy equilibria.

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Keywords

• Fixed point
• essential stable
• robust stable
• economy equilibrium

MSC

•  47H04
•  91A44

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