Vectorial Ekeland variational principle for cyclically antimonotone vector equilibrium problems. (2nd June 2020)

• Record Type: Journal Article
• Authors: Zhang, Chuang-liang; Huang, Nan-jing
• Is Part Of: Optimization. Volume 69:Number 6(2020)
• Page Start: 1255
• Page End: 1280
• Publication Date: 2020-06-02
• Subjects: Ekeland variational principle -- vector equilibrium problem -- triangle inequality property -- cyclic antimonotonicity -- vector variational inequality; 58E30 -- 49J40 -- 91B50 -- 58E35; Mathematical optimization -- Periodicals; 519.7
• DOI: 10.1080/02331934.2019.1689978
• Languages: English
• ISSNs: 0233-1934

Abstract

ABSTRACT: In this paper, we first obtain some results for the vectorial Ekeland variational principle with a W -distance, in which the final space is a real linear space not necessarily endowed with a topology. We introduce a cyclically antimonotone bifunction taking values in a real linear space, show its properties, and then apply the results to deduce a general vector equilibrium version of Ekeland variational principle. Moreover, we apply the properties of the cyclically antimonotone bifunction to study the existence of solutions for vector equilibrium problems defined on compact or noncompact sets. We also prove the existence of solutions for uncountable systems of vector equilibrium problems. Finally, our main results are applied to establish two new general versions of Caristi-Kirk fixed point theorem for set-valued mappings and some new existence theorems for vector variational inequalities under mild conditions.