Equilibrium versions of set-valued variational principles and their applications to organizational behavior

ABSTRACT

By using a pre-order principle in [Qiu JH. A pre-order principle and set-valued Ekeland variational principle. J Math Anal Appl. 2014;419:904–937], we establish a general equilibrium version of set-valued Ekeland variational principle (denoted by EVP), where the objective function is a set-valued bimap defined on the product of left-complete quasi-metric spaces and taking values in a quasi-ordered linear space, and the perturbation consists of a cone-convex subset of the ordering cone multiplied by the quasi-metric. Moreover, we obtain an equilibrium EVP, where the perturbation contains a σ-convex subset and the quasi-metric. From the above two general EVPs, we deduce several interesting corollaries, which extend and improve the related known results. Several examples show that the obtained set-valued EVPs are new. Finally, applying the above EVPs to organizational behavior sciences, we obtain some interesting results on organizational change and development with leadership. In particular, we show that the existence of robust organizational traps.

Keywords:

• Equilibrium version of Ekeland variational principle
• set-valued perturbation
• quasi-metric space
• organizational change
• existence of robust organizational traps

Mathematics Subject Classifications:

• 49J53
• 90C29

Acknowledgments

The authors are grateful to the reviewers for the favorable comments and helpful suggestions, which have greatly improved our paper.

Disclosure statement

No potential conflict of interest was reported by the authors.

Additional information

Funding

The first and third authors were supported by the National Natural Science Foundation of China [grant numbers 11471236, 11561049].